[{"year":"2025","date_created":"2026-06-29T12:59:46Z","issue":"10","publication_identifier":{"issn":["2330-0000"]},"doi":"10.1090/btran/186","publication":"Transactions of the American Mathematical Society, Series B","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2212.04969","open_access":"1"}],"extern":"1","author":[{"id":"c3bac823-112d-11f0-a3f5-c264f852e697","full_name":"Kuperberg, Vivian Zieve","first_name":"Vivian Zieve","last_name":"Kuperberg"},{"full_name":"Lalín, Matilde","first_name":"Matilde","last_name":"Lalín"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":12,"OA_place":"repository","mathsc":["11N60","05A15","11M50","11N56"],"page":"323-370","article_processing_charge":"No","abstract":[{"lang":"eng","text":"In Kuperberg and Lal´ın [Forum Math. 34 (2022), pp. 711–747],\r\nthe authors studied the mean-square of certain sums of the divisor function\r\ndk(f) over the function field Fq[T] in the limit as q →∞ and related these\r\nsums to integrals over the ensemble of symplectic matrices, along similar lines\r\nas previous work of Keating, Rodgers, Roditty-Gershon and Rudnick [Math. Z.\r\n288 (2018), pp. 167–198] for unitary matrices. We present an analogous problem yielding an integral over the ensemble of orthogonal matrices and pursue\r\na more detailed study of both the symplectic and orthogonal matrix integrals,\r\nrelating them to symmetric function theory. The function field results lead to\r\nconjectures concerning analogous questions over number fields."}],"publication_status":"published","external_id":{"arxiv":["2212.04969"]},"title":"Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime","OA_type":"green","status":"public","day":"20","citation":{"short":"V.Z. Kuperberg, M. Lalín, Transactions of the American Mathematical Society, Series B 12 (2025) 323–370.","ieee":"V. Z. Kuperberg and M. Lalín, “Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime,” <i>Transactions of the American Mathematical Society, Series B</i>, vol. 12, no. 10. American Mathematical Society, pp. 323–370, 2025.","ama":"Kuperberg VZ, Lalín M. Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime. <i>Transactions of the American Mathematical Society, Series B</i>. 2025;12(10):323-370. doi:<a href=\"https://doi.org/10.1090/btran/186\">10.1090/btran/186</a>","ista":"Kuperberg VZ, Lalín M. 2025. Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime. Transactions of the American Mathematical Society, Series B. 12(10), 323–370.","chicago":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Symplectic Conjectures for Sums of Divisor Functions and Explorations of an Orthogonal Regime.” <i>Transactions of the American Mathematical Society, Series B</i>. American Mathematical Society, 2025. <a href=\"https://doi.org/10.1090/btran/186\">https://doi.org/10.1090/btran/186</a>.","apa":"Kuperberg, V. Z., &#38; Lalín, M. (2025). Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime. <i>Transactions of the American Mathematical Society, Series B</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/btran/186\">https://doi.org/10.1090/btran/186</a>","mla":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Symplectic Conjectures for Sums of Divisor Functions and Explorations of an Orthogonal Regime.” <i>Transactions of the American Mathematical Society, Series B</i>, vol. 12, no. 10, American Mathematical Society, 2025, pp. 323–70, doi:<a href=\"https://doi.org/10.1090/btran/186\">10.1090/btran/186</a>."},"article_type":"original","oa_version":"Preprint","intvolume":"        12","type":"journal_article","_id":"22200","scopus_import":"1","oa":1,"month":"03","language":[{"iso":"eng"}],"date_published":"2025-03-20T00:00:00Z","publisher":"American Mathematical Society","arxiv":1,"date_updated":"2026-07-14T11:24:55Z"},{"day":"01","status":"public","OA_type":"green","citation":{"ieee":"V. Z. Kuperberg and M. Lalín, “Arithmetic constants for symplectic variances of the divisor function,” <i>Mathematika</i>, vol. 71, no. 3. Wiley, 2025.","short":"V.Z. Kuperberg, M. Lalín, Mathematika 71 (2025).","ista":"Kuperberg VZ, Lalín M. 2025. Arithmetic constants for symplectic variances of the divisor function. Mathematika. 71(3), e70029.","ama":"Kuperberg VZ, Lalín M. Arithmetic constants for symplectic variances of the divisor function. <i>Mathematika</i>. 2025;71(3). doi:<a href=\"https://doi.org/10.1112/mtk.70029\">10.1112/mtk.70029</a>","apa":"Kuperberg, V. Z., &#38; Lalín, M. (2025). Arithmetic constants for symplectic variances of the divisor function. <i>Mathematika</i>. Wiley. <a href=\"https://doi.org/10.1112/mtk.70029\">https://doi.org/10.1112/mtk.70029</a>","chicago":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Arithmetic Constants for Symplectic Variances of the Divisor Function.” <i>Mathematika</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/mtk.70029\">https://doi.org/10.1112/mtk.70029</a>.","mla":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Arithmetic Constants for Symplectic Variances of the Divisor Function.” <i>Mathematika</i>, vol. 71, no. 3, e70029, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/mtk.70029\">10.1112/mtk.70029</a>."},"scopus_import":"1","_id":"22199","oa_version":"Preprint","intvolume":"        71","article_type":"original","type":"journal_article","date_published":"2025-05-01T00:00:00Z","month":"05","language":[{"iso":"eng"}],"date_updated":"2026-07-14T11:20:10Z","publisher":"Wiley","arxiv":1,"oa":1,"publication_identifier":{"issn":["0025-5793","2041-7942"]},"doi":"10.1112/mtk.70029","issue":"3","publication":"Mathematika","date_created":"2026-06-29T12:59:16Z","year":"2025","article_number":"e70029","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.17939","open_access":"1"}],"quality_controlled":"1","mathsc":["11N60","05A15","11M50","11N56"],"author":[{"full_name":"Kuperberg, Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697","first_name":"Vivian Zieve","last_name":"Kuperberg"},{"full_name":"Lalín, Matilde","first_name":"Matilde","last_name":"Lalín"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","volume":71,"OA_place":"repository","title":"Arithmetic constants for symplectic variances of the divisor function","article_processing_charge":"No","external_id":{"arxiv":["2410.17939"]},"publication_status":"published","abstract":[{"text":"Kuperberg and Lalín stated some conjectures on the variance of certain sums of the divisor function dk(n) over number fields, which were inspired by analogous results over function fields proven by the authors. These problems are related to certain symplectic matrix integrals. While the function field results can be directly related to the random matrix integrals, the connection between the random matrix integrals and the number field results is less direct and involves arithmetic factors. The goal of this article is to give heuristic arguments for the formulas of these arithmetic factors.","lang":"eng"}]},{"citation":{"ieee":"R. de la Bretèche and V. Z. Kuperberg, “Lower bounds on weighted moments of primes in short intervals in number fields,” <i>Israel Journal of Mathematics</i>, vol. 267, no. 1. Springer Nature, pp. 437–461, 2025.","short":"R. de la Bretèche, V.Z. Kuperberg, Israel Journal of Mathematics 267 (2025) 437–461.","ista":"de la Bretèche R, Kuperberg VZ. 2025. Lower bounds on weighted moments of primes in short intervals in number fields. Israel Journal of Mathematics. 267(1), 437–461.","ama":"de la Bretèche R, Kuperberg VZ. Lower bounds on weighted moments of primes in short intervals in number fields. <i>Israel Journal of Mathematics</i>. 2025;267(1):437-461. doi:<a href=\"https://doi.org/10.1007/s11856-024-2711-0\">10.1007/s11856-024-2711-0</a>","apa":"de la Bretèche, R., &#38; Kuperberg, V. Z. (2025). Lower bounds on weighted moments of primes in short intervals in number fields. <i>Israel Journal of Mathematics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11856-024-2711-0\">https://doi.org/10.1007/s11856-024-2711-0</a>","chicago":"Bretèche, Régis de la, and Vivian Zieve Kuperberg. “Lower Bounds on Weighted Moments of Primes in Short Intervals in Number Fields.” <i>Israel Journal of Mathematics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s11856-024-2711-0\">https://doi.org/10.1007/s11856-024-2711-0</a>.","mla":"de la Bretèche, Régis, and Vivian Zieve Kuperberg. “Lower Bounds on Weighted Moments of Primes in Short Intervals in Number Fields.” <i>Israel Journal of Mathematics</i>, vol. 267, no. 1, Springer Nature, 2025, pp. 437–61, doi:<a href=\"https://doi.org/10.1007/s11856-024-2711-0\">10.1007/s11856-024-2711-0</a>."},"day":"01","status":"public","OA_type":"green","date_published":"2025-06-01T00:00:00Z","language":[{"iso":"eng"}],"month":"06","date_updated":"2026-07-14T11:28:49Z","arxiv":1,"publisher":"Springer Nature","oa":1,"scopus_import":"1","_id":"22201","intvolume":"       267","oa_version":"Preprint","article_type":"original","type":"journal_article","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2305.02662","open_access":"1"}],"quality_controlled":"1","publication_identifier":{"issn":["0021-2172"],"eissn":["1565-8511"]},"doi":"10.1007/s11856-024-2711-0","issue":"1","publication":"Israel Journal of Mathematics","date_created":"2026-06-29T13:00:06Z","year":"2025","title":"Lower bounds on weighted moments of primes in short intervals in number fields","article_processing_charge":"No","page":"437-461","publication_status":"published","external_id":{"arxiv":["2305.02662"]},"abstract":[{"text":"We consider an analog of a conjecture of Montgomery and Soundararajan on the moments of primes in short intervals in number fields; this analog was discussed and heuristically derived in a paper of the second author, Rodgers, and Roditty-Gershon. Adapting work of the first author and Fiorilli in the integer case, we establish lower bounds on a weighted version of these moments which agree with the conjectured values.","lang":"eng"}],"author":[{"first_name":"Régis","last_name":"de la Bretèche","full_name":"de la Bretèche, Régis"},{"last_name":"Kuperberg","first_name":"Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697","full_name":"Kuperberg, Vivian Zieve"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","volume":267,"OA_place":"repository"},{"citation":{"mla":"Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.” <i>Proceedings of the London Mathematical Society</i>, vol. 131, no. 1, e70068, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/plms.70068\">10.1112/plms.70068</a>.","chicago":"Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/plms.70068\">https://doi.org/10.1112/plms.70068</a>.","apa":"Bloom, T. F., &#38; Kuperberg, V. Z. (2025). Odd moments and adding fractions. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70068\">https://doi.org/10.1112/plms.70068</a>","ama":"Bloom TF, Kuperberg VZ. Odd moments and adding fractions. <i>Proceedings of the London Mathematical Society</i>. 2025;131(1). doi:<a href=\"https://doi.org/10.1112/plms.70068\">10.1112/plms.70068</a>","ista":"Bloom TF, Kuperberg VZ. 2025. Odd moments and adding fractions. Proceedings of the London Mathematical Society. 131(1), e70068.","ieee":"T. F. Bloom and V. Z. Kuperberg, “Odd moments and adding fractions,” <i>Proceedings of the London Mathematical Society</i>, vol. 131, no. 1. Wiley, 2025.","short":"T.F. Bloom, V.Z. Kuperberg, Proceedings of the London Mathematical Society 131 (2025)."},"OA_type":"green","day":"01","status":"public","oa":1,"language":[{"iso":"eng"}],"month":"07","date_published":"2025-07-01T00:00:00Z","publisher":"Wiley","arxiv":1,"date_updated":"2026-07-14T11:45:18Z","article_type":"original","intvolume":"       131","oa_version":"Preprint","type":"journal_article","_id":"22203","scopus_import":"1","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2312.09021"}],"year":"2025","date_created":"2026-06-29T13:00:46Z","article_number":"e70068","issue":"1","publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"doi":"10.1112/plms.70068","publication":"Proceedings of the London Mathematical Society","article_processing_charge":"No","abstract":[{"lang":"eng","text":"We prove near-optimal upper bounds for the oddmoments of the distribution of coprime residues inshort intervals, confirming a conjecture of Montgomeryand Vaughan. As an application, we prove near-optimalupper bounds for the average of the refined singularseries in the Hardy–Littlewood conjectures concerningthe number of prime 𝑘-tuples for 𝑘 odd. The mainnew ingredient is a near-optimal upper bound for thenumber of solutions to ∑1 ⩽𝑖 ⩽𝑘𝑎 𝑖𝑞𝑖∈ ℤ when 𝑘 is odd,with gcd(𝑎𝑖 , 𝑞𝑖 ) = 1 and restrictions on the size of thenumerators and denominators, which is of indepen-dent interest."}],"publication_status":"published","external_id":{"arxiv":["2312.09021"]},"title":"Odd moments and adding fractions","extern":"1","author":[{"full_name":"Bloom, Thomas F.","first_name":"Thomas F.","last_name":"Bloom"},{"first_name":"Vivian Zieve","last_name":"Kuperberg","full_name":"Kuperberg, Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":131,"OA_place":"repository","mathsc":["11N69","11N05","14G05"]},{"title":"Positive density for consecutive runs of sums of two squares","page":"1995-2046","article_processing_charge":"No","abstract":[{"text":"We study the distribution of consecutive sums of two squares in arithmetic progressions. We\r\nshow that for any odd squarefree modulus q, any two reduced congruence classes a1 and a2 mod q,\r\nand any r1,r2 ≥ 1, a positive density of sums of two squares begin a chain of r1 consecutive sums of\r\ntwo squares, all of which are a1 mod q, followed immediately by a chain of r2 consecutive sums of two\r\nsquares, all of which are a2 mod q. This is an analog of the result of Maynard for the sequence of primes,\r\nshowing that for any reduced congruence class a mod q and for any r ≥ 1, a positive density of primes\r\nbegin a sequence of r consecutive primes, all of which are a mod q","lang":"eng"}],"external_id":{"arxiv":["2406.04174"]},"publication_status":"published","extern":"1","author":[{"first_name":"Noam","last_name":"Kimmel","full_name":"Kimmel, Noam"},{"id":"c3bac823-112d-11f0-a3f5-c264f852e697","full_name":"Kuperberg, Vivian Zieve","first_name":"Vivian Zieve","last_name":"Kuperberg"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_place":"repository","volume":24,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2406.04174","open_access":"1"}],"quality_controlled":"1","issue":"5","doi":"10.1017/s1474748025000131","publication_identifier":{"issn":["1474-7480"],"eissn":["1475-3030"]},"publication":"Journal of the Institute of Mathematics of Jussieu","year":"2025","date_created":"2026-06-29T13:01:08Z","language":[{"iso":"eng"}],"month":"09","date_published":"2025-09-01T00:00:00Z","publisher":"Cambridge University Press","arxiv":1,"date_updated":"2026-07-14T11:50:36Z","oa":1,"_id":"22204","scopus_import":"1","article_type":"original","intvolume":"        24","oa_version":"Preprint","type":"journal_article","citation":{"apa":"Kimmel, N., &#38; Kuperberg, V. Z. (2025). Positive density for consecutive runs of sums of two squares. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s1474748025000131\">https://doi.org/10.1017/s1474748025000131</a>","chicago":"Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive Runs of Sums of Two Squares.” <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/s1474748025000131\">https://doi.org/10.1017/s1474748025000131</a>.","mla":"Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive Runs of Sums of Two Squares.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 24, no. 5, Cambridge University Press, 2025, pp. 1995–2046, doi:<a href=\"https://doi.org/10.1017/s1474748025000131\">10.1017/s1474748025000131</a>.","short":"N. Kimmel, V.Z. Kuperberg, Journal of the Institute of Mathematics of Jussieu 24 (2025) 1995–2046.","ieee":"N. Kimmel and V. Z. Kuperberg, “Positive density for consecutive runs of sums of two squares,” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 24, no. 5. Cambridge University Press, pp. 1995–2046, 2025.","ista":"Kimmel N, Kuperberg VZ. 2025. Positive density for consecutive runs of sums of two squares. Journal of the Institute of Mathematics of Jussieu. 24(5), 1995–2046.","ama":"Kimmel N, Kuperberg VZ. Positive density for consecutive runs of sums of two squares. <i>Journal of the Institute of Mathematics of Jussieu</i>. 2025;24(5):1995-2046. doi:<a href=\"https://doi.org/10.1017/s1474748025000131\">10.1017/s1474748025000131</a>"},"status":"public","day":"01","OA_type":"green"},{"date_updated":"2026-07-15T07:21:38Z","publisher":"American Physical Society","arxiv":1,"date_published":"2025-08-22T00:00:00Z","language":[{"iso":"eng"}],"month":"08","oa":1,"scopus_import":"1","_id":"22213","type":"journal_article","oa_version":"Published Version","intvolume":"        15","article_type":"original","citation":{"mla":"Lefranc, Thibault, et al. “Synthetic Quorum Sensing and Absorbing Phase Transitions in Colloidal Active Matter.” <i>Physical Review X</i>, vol. 15, no. 3, 031050, American Physical Society, 2025, doi:<a href=\"https://doi.org/10.1103/8csn-71jk\">10.1103/8csn-71jk</a>.","chicago":"Lefranc, Thibault, Alberto Dinelli, Carla Fernández-Rico, Roel P. A. Dullens, Julien Tailleur, and Denis Bartolo. “Synthetic Quorum Sensing and Absorbing Phase Transitions in Colloidal Active Matter.” <i>Physical Review X</i>. American Physical Society, 2025. <a href=\"https://doi.org/10.1103/8csn-71jk\">https://doi.org/10.1103/8csn-71jk</a>.","apa":"Lefranc, T., Dinelli, A., Fernández-Rico, C., Dullens, R. P. A., Tailleur, J., &#38; Bartolo, D. (2025). Synthetic quorum sensing and absorbing phase transitions in colloidal active matter. <i>Physical Review X</i>. American Physical Society. <a href=\"https://doi.org/10.1103/8csn-71jk\">https://doi.org/10.1103/8csn-71jk</a>","ama":"Lefranc T, Dinelli A, Fernández-Rico C, Dullens RPA, Tailleur J, Bartolo D. Synthetic quorum sensing and absorbing phase transitions in colloidal active matter. <i>Physical Review X</i>. 2025;15(3). doi:<a href=\"https://doi.org/10.1103/8csn-71jk\">10.1103/8csn-71jk</a>","ista":"Lefranc T, Dinelli A, Fernández-Rico C, Dullens RPA, Tailleur J, Bartolo D. 2025. Synthetic quorum sensing and absorbing phase transitions in colloidal active matter. Physical Review X. 15(3), 031050.","ieee":"T. Lefranc, A. Dinelli, C. Fernández-Rico, R. P. A. Dullens, J. Tailleur, and D. Bartolo, “Synthetic quorum sensing and absorbing phase transitions in colloidal active matter,” <i>Physical Review X</i>, vol. 15, no. 3. American Physical Society, 2025.","short":"T. Lefranc, A. Dinelli, C. Fernández-Rico, R.P.A. Dullens, J. Tailleur, D. Bartolo, Physical Review X 15 (2025)."},"day":"22","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"OA_type":"hybrid","title":"Synthetic quorum sensing and absorbing phase transitions in colloidal active matter","external_id":{"arxiv":["2502.13919"]},"publication_status":"published","abstract":[{"text":"Unlike biological active matter that constantly adapt to their environment, the motors of synthetic active particles are typically agnostic to their surroundings and merely operate at constant force. Here, we design colloidal active rods capable of modulating their inner activity in response to crowding, thereby enforcing a primitive form of quorum sensing interactions. Through experiments, simulations, and theory we elucidate the impact of these interactions on the phase behavior of isotropic active matter. We demonstrate that, when conditioned to density, motility regulation can either lead to an absorbing phase transition, where all particles freeze their dynamics, or to atypical phase separation, where flat interfaces supporting a net pressure drop are in mechanical equilibrium. Fully active and fully arrested particles can then form heterogeneous patterns ruled by the competition between quorum sensing and mechanical interactions. Beyond the specifics of motile colloids, we expect our findings to apply broadly to adaptive active matter assembled from living or synthetic units.","lang":"eng"}],"article_processing_charge":"No","volume":15,"OA_place":"publisher","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Lefranc, Thibault","first_name":"Thibault","last_name":"Lefranc"},{"full_name":"Dinelli, Alberto","first_name":"Alberto","last_name":"Dinelli"},{"id":"492def71-6250-11f0-b278-d41dbd241b62","full_name":"Fernández-Rico, Carla","first_name":"Carla","last_name":"Fernández-Rico"},{"full_name":"Dullens, Roel P. A.","last_name":"Dullens","first_name":"Roel P. A."},{"full_name":"Tailleur, Julien","last_name":"Tailleur","first_name":"Julien"},{"last_name":"Bartolo","first_name":"Denis","full_name":"Bartolo, Denis"}],"extern":"1","ddc":["530"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1103/8csn-71jk"}],"has_accepted_license":"1","quality_controlled":"1","publication":"Physical Review X","publication_identifier":{"issn":["2160-3308"]},"doi":"10.1103/8csn-71jk","issue":"3","article_number":"031050","date_created":"2026-06-30T06:32:31Z","year":"2025"},{"pmid":1,"volume":21,"author":[{"first_name":"José","last_name":"Fojo","full_name":"Fojo, José"},{"last_name":"Subert","first_name":"Rodolfo","full_name":"Subert, Rodolfo"},{"last_name":"Rodríguez-Arco","first_name":"Laura","full_name":"Rodríguez-Arco, Laura"},{"full_name":"López-López, Modesto T.","first_name":"Modesto T.","last_name":"López-López"},{"full_name":"Dijkstra, Marjolein","last_name":"Dijkstra","first_name":"Marjolein"},{"full_name":"Fernández-Rico, Carla","id":"492def71-6250-11f0-b278-d41dbd241b62","first_name":"Carla","last_name":"Fernández-Rico"},{"full_name":"Alvarez, Laura","first_name":"Laura","last_name":"Alvarez"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","title":"Field-driven reversible networks from colloidal rods","publication_status":"published","external_id":{"pmid":["40314070"]},"abstract":[{"lang":"eng","text":"Highly interconnected percolated networks are interesting structures for materials with enhanced transport and mechanical properties. While percolated networks of anisotropic particles have been explored at the nanoscale, achieving highly interconnected structures at the microscale remains challenging. In this work, we explore the controlled assembly of rod-like polymer colloids under external fields leading to reversible quasi-2D networks. By varying voltage and frequency, we modulate the pore size and thickness of the network. We find that field-driven attractive interactions enable percolation at lower area fractions than predicted for non-interacting rods. Monte Carlo simulations incorporating dipolar interactions and electrostatic boundary conditions confirm the field-induced transition from isotropic to aligned rod configurations, supporting the emergence of percolated networks. This work presents a simple and robust approach for assembling reconfigurable colloidal networks with controlled connectivity, offering new strategies for designing adaptive soft materials."}],"article_processing_charge":"No","page":"4596-4605","publication":"Soft Matter","doi":"10.1039/d5sm00218d","publication_identifier":{"eissn":["1744-6848"],"issn":["1744-683X"]},"issue":"23","date_created":"2026-06-30T06:32:50Z","year":"2025","quality_controlled":"1","scopus_import":"1","_id":"22214","type":"journal_article","intvolume":"        21","oa_version":"None","article_type":"original","date_updated":"2026-07-15T07:37:27Z","publisher":"Royal Society of Chemistry","date_published":"2025-06-21T00:00:00Z","language":[{"iso":"eng"}],"month":"06","status":"public","day":"21","OA_type":"closed access","citation":{"mla":"Fojo, José, et al. “Field-Driven Reversible Networks from Colloidal Rods.” <i>Soft Matter</i>, vol. 21, no. 23, Royal Society of Chemistry, 2025, pp. 4596–605, doi:<a href=\"https://doi.org/10.1039/d5sm00218d\">10.1039/d5sm00218d</a>.","apa":"Fojo, J., Subert, R., Rodríguez-Arco, L., López-López, M. T., Dijkstra, M., Fernández-Rico, C., &#38; Alvarez, L. (2025). Field-driven reversible networks from colloidal rods. <i>Soft Matter</i>. Royal Society of Chemistry. <a href=\"https://doi.org/10.1039/d5sm00218d\">https://doi.org/10.1039/d5sm00218d</a>","chicago":"Fojo, José, Rodolfo Subert, Laura Rodríguez-Arco, Modesto T. López-López, Marjolein Dijkstra, Carla Fernández-Rico, and Laura Alvarez. “Field-Driven Reversible Networks from Colloidal Rods.” <i>Soft Matter</i>. Royal Society of Chemistry, 2025. <a href=\"https://doi.org/10.1039/d5sm00218d\">https://doi.org/10.1039/d5sm00218d</a>.","ista":"Fojo J, Subert R, Rodríguez-Arco L, López-López MT, Dijkstra M, Fernández-Rico C, Alvarez L. 2025. Field-driven reversible networks from colloidal rods. Soft Matter. 21(23), 4596–4605.","ama":"Fojo J, Subert R, Rodríguez-Arco L, et al. Field-driven reversible networks from colloidal rods. <i>Soft Matter</i>. 2025;21(23):4596-4605. doi:<a href=\"https://doi.org/10.1039/d5sm00218d\">10.1039/d5sm00218d</a>","short":"J. Fojo, R. Subert, L. Rodríguez-Arco, M.T. López-López, M. Dijkstra, C. Fernández-Rico, L. Alvarez, Soft Matter 21 (2025) 4596–4605.","ieee":"J. Fojo <i>et al.</i>, “Field-driven reversible networks from colloidal rods,” <i>Soft Matter</i>, vol. 21, no. 23. Royal Society of Chemistry, pp. 4596–4605, 2025."}},{"volume":155,"OA_place":"publisher","author":[{"last_name":"Naskręcki","first_name":"Bartosz","full_name":"Naskręcki, Bartosz"},{"full_name":"Verzobio, Matteo","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306","first_name":"Matteo","last_name":"Verzobio"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","keyword":["Elliptic curves","Néron models","division polynomials","height functions","discrete valuation rings"],"title":"Common valuations of division polynomials","publication_status":"published","external_id":{"arxiv":["2203.02015"],"isi":["001174907100001"]},"abstract":[{"lang":"eng","text":"In this note, we prove a formula for the cancellation exponent  kv,n between division polynomials  ψn  and  ϕn  associated with a sequence  {nP}n∈N of points on an elliptic curve  E  defined over a discrete valuation field  K. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields."}],"article_processing_charge":"Yes (via OA deal)","page":"1646-1660","das_tickbox":"0","publication":"Proceedings of the Royal Society of Edinburgh Section A: Mathematics","publication_identifier":{"issn":["0308-2105"],"eissn":["1473-7124"]},"doi":"10.1017/prm.2024.7","issue":"5","researchdata_availability":"no","date_created":"2023-01-16T11:45:22Z","year":"2025","ddc":["510"],"has_accepted_license":"1","quality_controlled":"1","file":[{"success":1,"creator":"dernst","file_name":"2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf","content_type":"application/pdf","date_created":"2025-12-30T06:45:47Z","date_updated":"2025-12-30T06:45:47Z","file_size":477624,"access_level":"open_access","checksum":"c5ec6e29aca2fb4533cb95fac409a0b2","relation":"main_file","file_id":"20878"}],"supplementarymaterial":"no","corr_author":"1","scopus_import":"1","_id":"12311","acknowledgement":"Silverman, and Paul Voutier for the comments on the earlier version of this paper. The first author acknowledges the support by Dioscuri programme initiated by the Max Planck Society, jointly managed with the National Science Centre (Poland), and mutually funded by the Polish Ministry of Science and Higher Education and the German Federal Ministry of Education and Research. The second author has been supported by MIUR (Italy) through PRIN 2017 ‘Geometric, algebraic and analytic methods in arithmetic’ and has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","type":"journal_article","oa_version":"Published Version","intvolume":"       155","article_type":"original","date_updated":"2026-07-16T08:43:40Z","arxiv":1,"publisher":"Cambridge University Press","department":[{"_id":"TiBr"}],"date_published":"2025-10-01T00:00:00Z","month":"10","language":[{"iso":"eng"}],"file_date_updated":"2025-12-30T06:45:47Z","oa":1,"isi":1,"status":"public","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"OA_type":"hybrid","ec_funded":1,"project":[{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413"}],"citation":{"mla":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, vol. 155, no. 5, Cambridge University Press, 2025, pp. 1646–60, doi:<a href=\"https://doi.org/10.1017/prm.2024.7\">10.1017/prm.2024.7</a>.","chicago":"Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/prm.2024.7\">https://doi.org/10.1017/prm.2024.7</a>.","apa":"Naskręcki, B., &#38; Verzobio, M. (2025). Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/prm.2024.7\">https://doi.org/10.1017/prm.2024.7</a>","ista":"Naskręcki B, Verzobio M. 2025. Common valuations of division polynomials. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 155(5), 1646–1660.","ama":"Naskręcki B, Verzobio M. Common valuations of division polynomials. <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>. 2025;155(5):1646-1660. doi:<a href=\"https://doi.org/10.1017/prm.2024.7\">10.1017/prm.2024.7</a>","short":"B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 155 (2025) 1646–1660.","ieee":"B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,” <i>Proceedings of the Royal Society of Edinburgh Section A: Mathematics</i>, vol. 155, no. 5. Cambridge University Press, pp. 1646–1660, 2025."},"PlanS_conform":"1"},{"oa":1,"file_date_updated":"2025-12-15T09:39:12Z","publisher":"American Physical Society","arxiv":1,"department":[{"_id":"OnHo"}],"date_updated":"2026-07-16T08:27:32Z","language":[{"iso":"eng"}],"month":"08","date_published":"2025-08-29T00:00:00Z","acknowledgement":"We thank B. Baragiola, A. Boubriak, M. Clark, M. Jones, and P. Skrzypczyk for useful discussions. H.S. acknowledges financial support from EPSRC Quantum Engineering Centre for Doctoral Training Grant No. EP/SO23607/1. E.L. acknowledges support from the Engineering and Physical Sciences Research Council (EPSRC) Hub in Quantum Computing and Simulation (EP/T001062/1). T.S. acknowledges that they received no funding in support of this research. M.P.S. acknowledges support from the EPSRC Quantum Engineering Centre for Doctoral Training EP/SO23607/1 and the European Commission through Starting Grant No. ERC-2018-STG803665 (PEQEM). G.R. acknowledges support from the Royal Commission for the Exhibition of 1851 through a Research Fellowship, from the European Commission through Starting Grant No. ERC-2018-STG803665 (PEQEM) and Advanced Grant No. ERC-2020-ADG101021085 (FLQuant), and from EPSRC through Standard Proposal Grant No. EP/X016218/1 (Mono-Squeeze).","type":"journal_article","article_type":"original","intvolume":"        24","oa_version":"Published Version","_id":"20797","scopus_import":"1","PlanS_conform":"1","citation":{"ista":"Seabrook H, Lavie E, Strömberg KT, Stafford MP, Rubino G. 2025. Surpassing the loss-noise robustness trade-off in quantum key distribution. Physical Review Applied. 24(2), 024072.","ama":"Seabrook H, Lavie E, Strömberg KT, Stafford MP, Rubino G. Surpassing the loss-noise robustness trade-off in quantum key distribution. <i>Physical Review Applied</i>. 2025;24(2). doi:<a href=\"https://doi.org/10.1103/xq2l-r4r7\">10.1103/xq2l-r4r7</a>","ieee":"H. Seabrook, E. Lavie, K. T. Strömberg, M. P. Stafford, and G. Rubino, “Surpassing the loss-noise robustness trade-off in quantum key distribution,” <i>Physical Review Applied</i>, vol. 24, no. 2. American Physical Society, 2025.","short":"H. Seabrook, E. Lavie, K.T. Strömberg, M.P. Stafford, G. Rubino, Physical Review Applied 24 (2025).","mla":"Seabrook, Hannah, et al. “Surpassing the Loss-Noise Robustness Trade-off in Quantum Key Distribution.” <i>Physical Review Applied</i>, vol. 24, no. 2, 024072, American Physical Society, 2025, doi:<a href=\"https://doi.org/10.1103/xq2l-r4r7\">10.1103/xq2l-r4r7</a>.","apa":"Seabrook, H., Lavie, E., Strömberg, K. T., Stafford, M. P., &#38; Rubino, G. (2025). Surpassing the loss-noise robustness trade-off in quantum key distribution. <i>Physical Review Applied</i>. American Physical Society. <a href=\"https://doi.org/10.1103/xq2l-r4r7\">https://doi.org/10.1103/xq2l-r4r7</a>","chicago":"Seabrook, Hannah, Emilien Lavie, Karl T Strömberg, Matthew P. Stafford, and Giulia Rubino. “Surpassing the Loss-Noise Robustness Trade-off in Quantum Key Distribution.” <i>Physical Review Applied</i>. American Physical Society, 2025. <a href=\"https://doi.org/10.1103/xq2l-r4r7\">https://doi.org/10.1103/xq2l-r4r7</a>."},"OA_type":"hybrid","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"29","status":"public","abstract":[{"lang":"eng","text":"Quantum key distribution (QKD) offers a theoretically secure method to share secret keys, yet practical implementations face challenges due to noise and loss over long-distance channels. Traditional QKD protocols require extensive noise compensation, hindering their industrial scalability and lowering the achievable key rates. Alternative protocols encode logical qubits in noise-resilient states but at the cost of using many physical qubits, increasing susceptibility to loss and limiting transmission distance. In this work, we introduce a logical-qubit encoding that uses antisymmetric Bell states in the continuous photonic degrees of freedom, frequency and time. By leveraging the continuous space, we overcome this noise-loss robustness trade-off by minimizing the number of photons per logical qubit while optimizing the encoding resilience over noise fluctuations. We analyze the security of our encoding and demonstrate its robustness compared to existing state-of-the-art protocols. This approach provides a path toward scalable, efficient QKD implementations under realistic noise conditions."}],"publication_status":"published","external_id":{"arxiv":["2412.08694"]},"article_processing_charge":"Yes (in subscription journal)","title":"Surpassing the loss-noise robustness trade-off in quantum key distribution","volume":24,"OA_place":"publisher","author":[{"last_name":"Seabrook","first_name":"Hannah","full_name":"Seabrook, Hannah"},{"last_name":"Lavie","first_name":"Emilien","full_name":"Lavie, Emilien"},{"first_name":"Karl T","last_name":"Strömberg","full_name":"Strömberg, Karl T","id":"68011cd2-da32-11ee-a930-b2774c7aba5f"},{"first_name":"Matthew P.","last_name":"Stafford","full_name":"Stafford, Matthew P."},{"full_name":"Rubino, Giulia","last_name":"Rubino","first_name":"Giulia"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","quality_controlled":"1","file":[{"file_id":"20824","relation":"main_file","checksum":"12ddb0414780f65b8e690fe0e6cfb95e","access_level":"open_access","date_updated":"2025-12-15T09:39:12Z","file_size":3028735,"date_created":"2025-12-15T09:39:12Z","content_type":"application/pdf","file_name":"2025_PhysReviewApplied_Seabrook.pdf","creator":"dernst","success":1}],"supplementarymaterial":"no","ddc":["530"],"has_accepted_license":"1","researchdata_availability":"yes","article_number":"024072","year":"2025","date_created":"2025-12-11T10:46:28Z","publication":"Physical Review Applied","das_tickbox":"1","issue":"2","doi":"10.1103/xq2l-r4r7","dataavailabilitystatement":"The data that support the findings of this article are openly available at https://github.com/hmis4/SurpassingLNTradeOffQKD; https://github.com/hmis4/SurpassingLNTradeOffQKD/tree/main/DomainEngineering  ","publication_identifier":{"eissn":["2331-7019"]}},{"has_accepted_license":"1","ddc":["510"],"corr_author":"1","supplementarymaterial":"no","file":[{"file_id":"21300","access_level":"open_access","checksum":"e50a60a4303b81563f7adbcadbe2e986","relation":"main_file","file_size":1505580,"date_updated":"2026-02-17T11:56:20Z","date_created":"2026-02-17T11:56:20Z","file_name":"2025_AlgebraNumberTheory_Browning.pdf","content_type":"application/pdf","success":1,"creator":"dernst"}],"quality_controlled":"1","issue":"10","doi":"10.2140/ant.2025.19.2049","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"publication":"Algebra & Number Theory","das_tickbox":"0","year":"2025","date_created":"2026-02-16T15:22:19Z","researchdata_availability":"no","title":"Paucity of rational points on fibrations with multiple fibres","page":"2049-2090","article_processing_charge":"No","abstract":[{"lang":"eng","text":"Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allowed. We use log geometry to formulate a new sparsity criterion for the existence of everywhere locally soluble fibres and formulate new conjectures that generalise previous work of Loughran and Smeets. These conjectures involve geometric invariants of the associated multiplicity orbifolds on the base of the fibration in the spirit of Campana. We give evidence for the conjectures by providing an assortment of bounds using Chebotarev’s theorem and sieve methods, with most of the evidence involving upper bounds. "}],"publication_status":"published","external_id":{"arxiv":["2310.01135"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"full_name":"Lyczak, Julian","last_name":"Lyczak","first_name":"Julian"},{"last_name":"Smeets","first_name":"Arne","full_name":"Smeets, Arne"}],"volume":19,"OA_place":"publisher","PlanS_conform":"1","citation":{"ieee":"T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations with multiple fibres,” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10. Mathematical Sciences Publishers, pp. 2049–2090, 2025.","short":"T.D. Browning, J. Lyczak, A. Smeets, Algebra &#38; Number Theory 19 (2025) 2049–2090.","ama":"Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. 2025;19(10):2049-2090. doi:<a href=\"https://doi.org/10.2140/ant.2025.19.2049\">10.2140/ant.2025.19.2049</a>","ista":"Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations with multiple fibres. Algebra &#38; Number Theory. 19(10), 2049–2090.","apa":"Browning, T. D., Lyczak, J., &#38; Smeets, A. (2025). Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2025.19.2049\">https://doi.org/10.2140/ant.2025.19.2049</a>","chicago":"Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/ant.2025.19.2049\">https://doi.org/10.2140/ant.2025.19.2049</a>.","mla":"Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10, Mathematical Sciences Publishers, 2025, pp. 2049–90, doi:<a href=\"https://doi.org/10.2140/ant.2025.19.2049\">10.2140/ant.2025.19.2049</a>."},"project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","call_identifier":"FWF","name":"New frontiers of the Manin conjecture"}],"day":"05","status":"public","OA_type":"diamond","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"month":"09","language":[{"iso":"eng"}],"date_published":"2025-09-05T00:00:00Z","publisher":"Mathematical Sciences Publishers","arxiv":1,"department":[{"_id":"TiBr"}],"date_updated":"2026-07-16T08:52:36Z","oa":1,"file_date_updated":"2026-02-17T11:56:20Z","_id":"21244","article_type":"original","oa_version":"Published Version","intvolume":"        19","acknowledgement":"We are very grateful to Tim Santens for useful conversations and to the anonymous referees for numerous pertinent remarks. While working on this paper, Browning was supported by a FWF grant (DOI 10.55776/P32428), Lyczak was supported by UKRI MR/V021362/1, and Smeets was supported by grant G0B1721N of the Fund for Scientific Research – Flanders.","type":"journal_article"},{"scopus_import":"1","_id":"20850","acknowledgement":"The author would like to thank his supervisor Tim Browning for suggesting this project and many helpful conversations and useful comments. Moreover, he is grateful to Jakob Glas, Damaris Schindler, Igor Shparlinski, Matteo Verzobio, Victor Wang, Florian Wilsch and Shuntaro Yamagishi for taking their time to answer his questions and their valuable suggestions.","type":"journal_article","intvolume":"        37","oa_version":"Published Version","article_type":"original","date_updated":"2026-07-16T08:45:12Z","department":[{"_id":"TiBr"}],"arxiv":1,"publisher":"Université de Bordeaux","date_published":"2025-11-27T00:00:00Z","month":"11","language":[{"iso":"eng"}],"file_date_updated":"2025-12-29T10:05:22Z","oa":1,"status":"public","day":"27","tmp":{"short":"CC BY-ND (4.0)","image":"/image/cc_by_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)"},"OA_type":"hybrid","citation":{"ieee":"Y. Diao, “Class numbers and integer points on some Pellian surfaces,” <i>Journal de theorie des nombres de Bordeaux</i>, vol. 37, no. 3. Université de Bordeaux, pp. 973–988, 2025.","short":"Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988.","ama":"Diao Y. Class numbers and integer points on some Pellian surfaces. <i>Journal de theorie des nombres de Bordeaux</i>. 2025;37(3):973-988. doi:<a href=\"https://doi.org/10.5802/jtnb.1348\">10.5802/jtnb.1348</a>","ista":"Diao Y. 2025. Class numbers and integer points on some Pellian surfaces. Journal de theorie des nombres de Bordeaux. 37(3), 973–988.","chicago":"Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux, 2025. <a href=\"https://doi.org/10.5802/jtnb.1348\">https://doi.org/10.5802/jtnb.1348</a>.","apa":"Diao, Y. (2025). Class numbers and integer points on some Pellian surfaces. <i>Journal de Theorie Des Nombres de Bordeaux</i>. Université de Bordeaux. <a href=\"https://doi.org/10.5802/jtnb.1348\">https://doi.org/10.5802/jtnb.1348</a>","mla":"Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” <i>Journal de Theorie Des Nombres de Bordeaux</i>, vol. 37, no. 3, Université de Bordeaux, 2025, pp. 973–88, doi:<a href=\"https://doi.org/10.5802/jtnb.1348\">10.5802/jtnb.1348</a>."},"volume":37,"OA_place":"publisher","author":[{"id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b","orcid":"0000-0002-4989-5330","full_name":"Diao, Yijie","first_name":"Yijie","last_name":"Diao"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Class numbers and integer points on some Pellian surfaces","external_id":{"arxiv":["2408.03774"]},"publication_status":"published","abstract":[{"lang":"eng","text":"We provide an estimate for the number of nontrivial integer points on the Pellian surface t^2 - du^2 = 1 in a bounded region. We give a lower bound on the size of fundamental solutions for almost all d in a certain class, based on a recent conjecture of Browning and Wilsch about integer points on log K3 surfaces. We also obtain an upper bound on the average of class number in this class, assuming the same conjecture."},{"lang":"fre","text":"Nous donnons une estimation du nombre de points entiers non triviaux sur la surface pellienne \r\nt^2 - du^2 = 1 dans une région bornée. Nous établissons une borne inférieure pour la taille des solutions fondamentales pour presque tout d appartenant à une certaine classe, en nous fondant sur une conjecture récente de Browning et Wilsch concernant les points entiers sur les surfaces log K3. Nous obtenons également une borne supérieure pour la moyenne du nombre de classes dans cette classe, sous la même hypothèse conjecturale."}],"article_processing_charge":"Yes (in subscription journal)","page":"973-988","das_tickbox":"0","publication":"Journal de theorie des nombres de Bordeaux","doi":"10.5802/jtnb.1348","publication_identifier":{"eissn":["2118-8572"],"issn":["1246-7405"]},"issue":"3","researchdata_availability":"no","date_created":"2025-12-21T23:01:35Z","year":"2025","ddc":["510"],"has_accepted_license":"1","file":[{"date_updated":"2025-12-29T10:05:22Z","file_size":766196,"access_level":"open_access","checksum":"67aa0afbc0b5bcbff5341f4d25e6ba20","relation":"main_file","file_id":"20861","success":1,"creator":"dernst","file_name":"2025_JTNB_Diao.pdf","content_type":"application/pdf","date_created":"2025-12-29T10:05:22Z"}],"quality_controlled":"1","supplementarymaterial":"no","corr_author":"1"},{"date_published":"2025-09-01T00:00:00Z","language":[{"iso":"eng"}],"month":"09","date_updated":"2026-07-16T08:48:35Z","publisher":"Cambridge: Alliance of Diamond Open Access Journals","department":[{"_id":"TiBr"}],"arxiv":1,"file_date_updated":"2026-02-12T07:50:47Z","oa":1,"scopus_import":"1","_id":"21003","intvolume":"      2025","oa_version":"Published Version","article_type":"original","type":"journal_article","acknowledgement":"Supported by FWF grant (DOI 10.55776/P36278), Supported by European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant\r\nAgreement No. 101034413.","citation":{"mla":"Browning, Timothy D., and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” <i>Discrete Analysis</i>, vol. 2025, 12, Cambridge: Alliance of Diamond Open Access Journals, 2025, doi:<a href=\"https://doi.org/10.19086/da.143787\">10.19086/da.143787</a>.","apa":"Browning, T. D., &#38; Verzobio, M. (2025). Counting integer points on affine surfaces with a side condition. <i>Discrete Analysis</i>. Cambridge: Alliance of Diamond Open Access Journals. <a href=\"https://doi.org/10.19086/da.143787\">https://doi.org/10.19086/da.143787</a>","chicago":"Browning, Timothy D, and Matteo Verzobio. “Counting Integer Points on Affine Surfaces with a Side Condition.” <i>Discrete Analysis</i>. Cambridge: Alliance of Diamond Open Access Journals, 2025. <a href=\"https://doi.org/10.19086/da.143787\">https://doi.org/10.19086/da.143787</a>.","ama":"Browning TD, Verzobio M. Counting integer points on affine surfaces with a side condition. <i>Discrete Analysis</i>. 2025;2025. doi:<a href=\"https://doi.org/10.19086/da.143787\">10.19086/da.143787</a>","ista":"Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces with a side condition. Discrete Analysis. 2025, 12.","short":"T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025).","ieee":"T. D. Browning and M. Verzobio, “Counting integer points on affine surfaces with a side condition,” <i>Discrete Analysis</i>, vol. 2025. Cambridge: Alliance of Diamond Open Access Journals, 2025."},"project":[{"grant_number":"P36278","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory"},{"grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020"}],"status":"public","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ec_funded":1,"OA_type":"diamond","title":"Counting integer points on affine surfaces with a side condition","article_processing_charge":"No","external_id":{"arxiv":["2408.11453"]},"publication_status":"published","abstract":[{"lang":"eng","text":"We extend work of Heath-Brown and Salberger, based on the determinant method, to provide a uniform upper bound for the number of integral points of bounded height on an affine surface, which are subject to a polynomial congruence condition. This is applied to get a new uniform bound for points on diagonal quadric surfaces, and to a problem about the representation of integers as a sum of four unlike powers."}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning"},{"full_name":"Verzobio, Matteo","orcid":"0000-0002-0854-0306","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","first_name":"Matteo","last_name":"Verzobio"}],"OA_place":"publisher","volume":2025,"has_accepted_license":"1","ddc":["510"],"supplementarymaterial":"no","corr_author":"1","file":[{"success":1,"creator":"dernst","date_created":"2026-02-12T07:50:47Z","file_name":"2025_DiscreteAnalysis_Browning.pdf","content_type":"application/pdf","access_level":"open_access","checksum":"3d38e850b40f3e1abbfd30073bd4388a","relation":"main_file","date_updated":"2026-02-12T07:50:47Z","file_size":393625,"file_id":"21214"}],"publication_identifier":{"eissn":["2397-3129"]},"doi":"10.19086/da.143787","das_tickbox":"0","publication":"Discrete Analysis","date_created":"2026-01-18T23:02:44Z","year":"2025","article_number":"12","researchdata_availability":"no"},{"oa_version":"Published Version","article_type":"original","type":"journal_article","acknowledgement":"The first author would like to thank Samir Siksek for introducing the problem\r\nto him. The material in Section 6 is a result of discussing with many people, and the second author is very grateful to Tim Browning, Stephanie Chan, Jakob Glas, Jakub Löwit, Mirko Mauri, Marta Pieropan, Mike Roth, Matteo Verzobio and Victor Wang for taking the time to answer his questions and for their valuable suggestions. We thank Tim Browning, Yijie Diao, Ana Marija Vego and the anonymous referee for their helpful comments.\r\nThe first author was supported by NSERC Discovery Grant RGPIN-2024-06810. The\r\nsecond author was supported by the NWO Veni Grant 016.Veni.192.047 during his time at\r\nUtrecht University and by a FWF grant (DOI 10.55776/P32428) at the Institute of Science and\r\nTechnology Austria while working on this paper.","_id":"21260","oa":1,"date_published":"2025-08-06T00:00:00Z","language":[{"iso":"eng"}],"month":"08","date_updated":"2026-07-16T08:54:37Z","department":[{"_id":"TiBr"}],"publisher":"EMS Press","arxiv":1,"OA_type":"diamond","status":"public","day":"06","citation":{"mla":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1697\">10.4171/jems/1697</a>.","apa":"Yao Xiao, S., &#38; Yamagishi, S. (2025). Quartic polynomials in two variables do not represent all non-negative integers. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1697\">https://doi.org/10.4171/jems/1697</a>","chicago":"Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables Do Not Represent All Non-Negative Integers.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1697\">https://doi.org/10.4171/jems/1697</a>.","ama":"Yao Xiao S, Yamagishi S. Quartic polynomials in two variables do not represent all non-negative integers. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1697\">10.4171/jems/1697</a>","ista":"Yao Xiao S, Yamagishi S. 2025. Quartic polynomials in two variables do not represent all non-negative integers. Journal of the European Mathematical Society.","ieee":"S. Yao Xiao and S. Yamagishi, “Quartic polynomials in two variables do not represent all non-negative integers,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","short":"S. Yao Xiao, S. Yamagishi, Journal of the European Mathematical Society (2025)."},"project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","grant_number":"P32428","call_identifier":"FWF","name":"New frontiers of the Manin conjecture"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"full_name":"Yao Xiao, Stanley","first_name":"Stanley","last_name":"Yao Xiao"},{"last_name":"Yamagishi","first_name":"Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b","full_name":"Yamagishi, Shuntaro"}],"OA_place":"publisher","article_processing_charge":"No","external_id":{"arxiv":["2307.05712"]},"publication_status":"epub_ahead","abstract":[{"lang":"eng","text":"We prove that there does not exist F∈Q[x,y] of degree 4 such that F(Z^2 )=Z ≥0. In particular, this answers a question by John S. Lew and Bjorn Poonen for quartic polynomials."}],"title":"Quartic polynomials in two variables do not represent all non-negative integers","date_created":"2026-02-16T16:00:02Z","year":"2025","researchdata_availability":"no","publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"doi":"10.4171/jems/1697","das_tickbox":"0","publication":"Journal of the European Mathematical Society","supplementarymaterial":"no","corr_author":"1","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1697"}],"ddc":["500"]},{"_id":"18822","scopus_import":"1","type":"journal_article","acknowledgement":"I thank Peter Sarnak for suggesting projects that ultimately led to the present paper. I also thank him for many encouraging discussions, helpful comments, and references. Thanks also to Tim Browning, Trevor Wooley, and Nina Zubrilina for helpful comments, and to Levent Alpöge and Will Sawin for some interesting old discussions. I thank Yang Liu, Evan O'Dorney, Ashwin Sah, and Mark Sellke for conversations illuminating the combinatorics of an older, counting version of the present Lemma 4.9. Finally, special thanks are due to the editors and referees for their patience and help with the exposition. This work was partially supported by NSF Grant DMS-1802211, and the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","article_type":"original","intvolume":"        71","oa_version":"Published Version","department":[{"_id":"TiBr"}],"publisher":"London Mathematical Society","date_updated":"2026-07-16T09:14:24Z","month":"01","language":[{"iso":"eng"}],"date_published":"2025-01-02T00:00:00Z","oa":1,"file_date_updated":"2025-01-14T06:52:09Z","isi":1,"status":"public","day":"02","ec_funded":1,"OA_type":"hybrid","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"citation":{"apa":"Wang, V. (2025). Diagonal cubic forms and the large sieve. <i>Mathematika</i>. London Mathematical Society. <a href=\"https://doi.org/10.1112/mtk.70008\">https://doi.org/10.1112/mtk.70008</a>","chicago":"Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” <i>Mathematika</i>. London Mathematical Society, 2025. <a href=\"https://doi.org/10.1112/mtk.70008\">https://doi.org/10.1112/mtk.70008</a>.","mla":"Wang, Victor. “Diagonal Cubic Forms and the Large Sieve.” <i>Mathematika</i>, vol. 71, no. 1, e70008, London Mathematical Society, 2025, doi:<a href=\"https://doi.org/10.1112/mtk.70008\">10.1112/mtk.70008</a>.","short":"V. Wang, Mathematika 71 (2025).","ieee":"V. Wang, “Diagonal cubic forms and the large sieve,” <i>Mathematika</i>, vol. 71, no. 1. London Mathematical Society, 2025.","ista":"Wang V. 2025. Diagonal cubic forms and the large sieve. Mathematika. 71(1), e70008.","ama":"Wang V. Diagonal cubic forms and the large sieve. <i>Mathematika</i>. 2025;71(1). doi:<a href=\"https://doi.org/10.1112/mtk.70008\">10.1112/mtk.70008</a>"},"volume":71,"OA_place":"publisher","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","orcid":"0000-0002-0704-7026","full_name":"Wang, Victor","last_name":"Wang","first_name":"Victor"}],"title":"Diagonal cubic forms and the large sieve","abstract":[{"lang":"eng","text":"Let N(X) be the number of integral zeros (mathematical equation). Works of Hooley and Heath-Brown imply (mathematical equation), if one assumes automorphy and grand Riemann hypothesis for certain Hasse–Weil L-functions. Assuming instead a natural large sieve inequality, we recover the same bound on N(X). This is part of a more general statement, for diagonal cubic forms in (mathematical equation) variables, where we allow approximations to Hasse–Weil L-functions."}],"external_id":{"isi":["001388255500001"]},"publication_status":"published","article_processing_charge":"Yes (via OA deal)","publication":"Mathematika","das_tickbox":"0","issue":"1","doi":"10.1112/mtk.70008","publication_identifier":{"issn":["0025-5793"],"eissn":["2041-7942"]},"researchdata_availability":"no","article_number":"e70008","year":"2025","date_created":"2025-01-12T23:04:01Z","ddc":["510"],"has_accepted_license":"1","quality_controlled":"1","file":[{"file_id":"18845","file_size":309893,"date_updated":"2025-01-14T06:52:09Z","relation":"main_file","checksum":"700a8596b4bffce2320d074120962c22","access_level":"open_access","content_type":"application/pdf","file_name":"2025_Mathematika_Wang.pdf","date_created":"2025-01-14T06:52:09Z","creator":"dernst","success":1}],"corr_author":"1","supplementarymaterial":"no"},{"author":[{"first_name":"Shuntaro","last_name":"Yamagishi","full_name":"Yamagishi, Shuntaro","id":"0c3fbc5c-f7a6-11ec-8d70-9485e75b416b"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","volume":221,"OA_place":"repository","article_processing_charge":"No","page":"141-151","external_id":{"arxiv":["2304.02620"]},"publication_status":"published","abstract":[{"text":"Let F∈Z[x1,…,xn] be a homogeneous form of degree d≥2, and V∗F the singular locus of the hypersurface {x∈AnC:F(x)=0}. A longstanding result of Birch states that there is a non-trivial integral solution to the equation F(x1,…,xn)=0 provided n>dimV∗F+(d−1)2d, and there is a non-singular solution in R and Qp for all primes p. We give a different formulation of this result. More precisely, we replace dimV∗F with a quantity HF defined in terms of the Hessian matrix of F. This quantity satisfies 0≤HF≤dimV∗F; therefore, we improve on the aforementioned result of Birch if HF<dimV∗F. We also prove the corresponding result for systems of forms of equal degree.","lang":"eng"}],"keyword":["Diophantine equations","homogeneous forms"],"title":"Birch’s theorem on forms in many variables with a Hessian condition","date_created":"2026-04-26T22:01:48Z","year":"2025","researchdata_availability":"no","doi":"10.4064/aa241029-19-8","publication_identifier":{"issn":["0065-1036"],"eissn":["1730-6264"]},"issue":"2","das_tickbox":"0","publication":"Acta Arithmetica","supplementarymaterial":"no","corr_author":"1","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2304.02620","open_access":"1"}],"oa_version":"Preprint","intvolume":"       221","article_type":"original","acknowledgement":"The author would like to thank Tim Browning, Jakob Glas and Simon Rydin Myerson for useful suggestions and conversations. Finally, he would like to thank the anonymous referees for their helpful comments. The author was supported by the NWO Veni Grant 016.Veni.192.047 during his time at Utrecht University and by the FWF grant P 36278 at the Institute of Science and Technology Austria while working on this article.","type":"journal_article","scopus_import":"1","_id":"21768","oa":1,"date_published":"2025-10-28T00:00:00Z","month":"10","language":[{"iso":"eng"}],"date_updated":"2026-07-16T09:04:43Z","publisher":"Instytut Matematyczny","arxiv":1,"department":[{"_id":"TiBr"}],"OA_type":"green","status":"public","day":"28","citation":{"mla":"Yamagishi, Shuntaro. “Birch’s Theorem on Forms in Many Variables with a Hessian Condition.” <i>Acta Arithmetica</i>, vol. 221, no. 2, Instytut Matematyczny, 2025, pp. 141–51, doi:<a href=\"https://doi.org/10.4064/aa241029-19-8\">10.4064/aa241029-19-8</a>.","apa":"Yamagishi, S. (2025). Birch’s theorem on forms in many variables with a Hessian condition. <i>Acta Arithmetica</i>. Instytut Matematyczny. <a href=\"https://doi.org/10.4064/aa241029-19-8\">https://doi.org/10.4064/aa241029-19-8</a>","chicago":"Yamagishi, Shuntaro. “Birch’s Theorem on Forms in Many Variables with a Hessian Condition.” <i>Acta Arithmetica</i>. Instytut Matematyczny, 2025. <a href=\"https://doi.org/10.4064/aa241029-19-8\">https://doi.org/10.4064/aa241029-19-8</a>.","ista":"Yamagishi S. 2025. Birch’s theorem on forms in many variables with a Hessian condition. Acta Arithmetica. 221(2), 141–151.","ama":"Yamagishi S. Birch’s theorem on forms in many variables with a Hessian condition. <i>Acta Arithmetica</i>. 2025;221(2):141-151. doi:<a href=\"https://doi.org/10.4064/aa241029-19-8\">10.4064/aa241029-19-8</a>","short":"S. Yamagishi, Acta Arithmetica 221 (2025) 141–151.","ieee":"S. Yamagishi, “Birch’s theorem on forms in many variables with a Hessian condition,” <i>Acta Arithmetica</i>, vol. 221, no. 2. Instytut Matematyczny, pp. 141–151, 2025."},"project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"}]},{"researchdata_availability":"no","date_created":"2026-02-17T07:46:26Z","year":"2025","das_tickbox":"0","publication":"Journal of the European Mathematical Society","publication_identifier":{"issn":["1435-9855"],"eissn":["1435-9863"]},"doi":"10.4171/jems/1704","quality_controlled":"1","supplementarymaterial":"no","corr_author":"1","ddc":["510"],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/JEMS/1704"}],"OA_place":"publisher","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"first_name":"Timothy D","last_name":"Browning","full_name":"Browning, Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"},{"first_name":"Yik Tung","last_name":"Chan","full_name":"Chan, Yik Tung","orcid":"0000-0001-8467-4106","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1"}],"publication_status":"epub_ahead","external_id":{"arxiv":["2401.04375"]},"abstract":[{"lang":"eng","text":"For a given elliptic curve E in short Weierstrass form, we show that almost all quadratic twists E \r\nD have no integral points, as D ranges over square-free integers ordered by size. Our result is conditional on a weak form of the Hall–Lang conjecture in the case that E has partial 2-torsion. The proof uses a correspondence of Mordell and the reduction theory of binary quartic forms in order to transfer the problem to counting rational points of bounded height on a certain singular cubic surface, together with extensive use of cancellation in character sum estimates, drawn from Heath-Brown’s analysis of Selmer group statistics for the congruent number curve."}],"article_processing_charge":"No","title":"Almost all quadratic twists of an elliptic curve have no integral points","OA_type":"diamond","day":"17","status":"public","project":[{"name":"Rational curves via function field analytic number theory","_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","grant_number":"P36278"}],"citation":{"chicago":"Browning, Timothy D, and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/jems/1704\">https://doi.org/10.4171/jems/1704</a>.","apa":"Browning, T. D., &#38; Chan, S. (2025). Almost all quadratic twists of an elliptic curve have no integral points. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href=\"https://doi.org/10.4171/jems/1704\">https://doi.org/10.4171/jems/1704</a>","mla":"Browning, Timothy D., and Stephanie Chan. “Almost All Quadratic Twists of an Elliptic Curve Have No Integral Points.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href=\"https://doi.org/10.4171/jems/1704\">10.4171/jems/1704</a>.","ieee":"T. D. Browning and S. Chan, “Almost all quadratic twists of an elliptic curve have no integral points,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025.","short":"T.D. Browning, S. Chan, Journal of the European Mathematical Society (2025).","ista":"Browning TD, Chan S. 2025. Almost all quadratic twists of an elliptic curve have no integral points. Journal of the European Mathematical Society.","ama":"Browning TD, Chan S. Almost all quadratic twists of an elliptic curve have no integral points. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href=\"https://doi.org/10.4171/jems/1704\">10.4171/jems/1704</a>"},"type":"journal_article","acknowledgement":"The authors are grateful to Roger Heath-Brown and to the anonymous referees for useful comments. The first author was supported by an FWF grant (DOI 10.55776/P36278).","oa_version":"Published Version","article_type":"original","_id":"21266","DOAJ_listed":"1","oa":1,"date_updated":"2026-07-16T09:00:02Z","department":[{"_id":"TiBr"}],"publisher":"EMS Press","arxiv":1,"date_published":"2025-09-17T00:00:00Z","language":[{"iso":"eng"}],"month":"09"},{"citation":{"ama":"Wang V, Xu MW. Harper’s beyond square-root conjecture. <i>International Mathematics Research Notices</i>. 2025;2025(18). doi:<a href=\"https://doi.org/10.1093/imrn/rnaf279\">10.1093/imrn/rnaf279</a>","ista":"Wang V, Xu MW. 2025. Harper’s beyond square-root conjecture. International Mathematics Research Notices. 2025(18), rnaf279.","ieee":"V. Wang and M. W. Xu, “Harper’s beyond square-root conjecture,” <i>International Mathematics Research Notices</i>, vol. 2025, no. 18. Oxford University Press, 2025.","short":"V. Wang, M.W. Xu, International Mathematics Research Notices 2025 (2025).","mla":"Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.” <i>International Mathematics Research Notices</i>, vol. 2025, no. 18, rnaf279, Oxford University Press, 2025, doi:<a href=\"https://doi.org/10.1093/imrn/rnaf279\">10.1093/imrn/rnaf279</a>.","apa":"Wang, V., &#38; Xu, M. W. (2025). Harper’s beyond square-root conjecture. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnaf279\">https://doi.org/10.1093/imrn/rnaf279</a>","chicago":"Wang, Victor, and Max Wenqiang Xu. “Harper’s beyond Square-Root Conjecture.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2025. <a href=\"https://doi.org/10.1093/imrn/rnaf279\">https://doi.org/10.1093/imrn/rnaf279</a>."},"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"day":"01","status":"public","ec_funded":1,"OA_type":"green","language":[{"iso":"eng"}],"month":"09","date_published":"2025-09-01T00:00:00Z","publisher":"Oxford University Press","arxiv":1,"department":[{"_id":"TiBr"}],"date_updated":"2026-07-16T08:57:40Z","oa":1,"_id":"21265","scopus_import":"1","article_type":"original","oa_version":"Preprint","intvolume":"      2025","type":"journal_article","acknowledgement":"The first author is supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101034413. The second author is supported by a Simons Junior Fellowship from Simons Foundation. We thank Paul Bourgade and Kannan Soundararajan for discussions on random matrices and probability, Alexandra Florea for helpful comments on the Ratios Conjecture, and Joni Teräväinen for providing several references. We are also grateful to Alexandra Florea, Adam Harper, Joni Teräväinen, and the referee for helpful comments on earlier drafts.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2405.04094"}],"supplementarymaterial":"no","quality_controlled":"1","issue":"18","doi":"10.1093/imrn/rnaf279","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"publication":"International Mathematics Research Notices","das_tickbox":"0","year":"2025","date_created":"2026-02-17T07:45:45Z","researchdata_availability":"no","article_number":"rnaf279","title":"Harper’s beyond square-root conjecture","article_processing_charge":"No","abstract":[{"text":"We explain how the (shifted) Ratios Conjecture for $L(s,\\chi )$ would extend a randomization argument of Harper from a conductor-limited range to an unlimited range of “beyond square-root cancellation” for character twists of the Liouville function. As a corollary, the Liouville function would have nontrivial cancellation in arithmetic progressions of modulus just exceeding the well-known square-root barrier. Morally, the paper passes from random matrices to random multiplicative functions.","lang":"eng"}],"publication_status":"published","external_id":{"arxiv":["2405.04094"]},"author":[{"orcid":"0000-0002-0704-7026","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9","full_name":"Wang, Victor","last_name":"Wang","first_name":"Victor"},{"full_name":"Xu, Max Wenqiang","first_name":"Max Wenqiang","last_name":"Xu"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_place":"repository","volume":2025},{"intvolume":"        19","oa_version":"Published Version","article_type":"original","type":"journal_article","acknowledgement":"I am very grateful to my Ph.D. advisor Emmanuel Peyre for all the remarks and suggestions he made during the writing of this article. I warmly thank Margaret Bilu and Tim Browning for some valuable comments they made on a preliminary version of this work. I would like to thank David Bourqui as well for several helpful conversations. Finally, I thank the anonymous referee for their very careful reading and their numerous comments and suggestions which helped me a lot in improving the exposition, besides fixing several typos, and Elizabeth Weaver for the final editing work. During the revision process of this work, the author received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.","_id":"19054","file_date_updated":"2026-02-17T13:17:00Z","oa":1,"date_published":"2025-04-22T00:00:00Z","month":"04","language":[{"iso":"eng"}],"date_updated":"2026-07-16T09:23:01Z","publisher":"Mathematical Sciences Publishers","arxiv":1,"department":[{"_id":"TiBr"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"OA_type":"diamond","ec_funded":1,"status":"public","day":"22","citation":{"chicago":"Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products of Toric Varieties.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/ant.2025.19.883\">https://doi.org/10.2140/ant.2025.19.883</a>.","apa":"Faisant, L. (2025). Motivic distribution of rational curves and twisted products of toric varieties. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2025.19.883\">https://doi.org/10.2140/ant.2025.19.883</a>","mla":"Faisant, Loïs. “Motivic Distribution of Rational Curves and Twisted Products of Toric Varieties.” <i>Algebra &#38; Number Theory</i>, vol. 19, Mathematical Sciences Publishers, 2025, pp. 883–965, doi:<a href=\"https://doi.org/10.2140/ant.2025.19.883\">10.2140/ant.2025.19.883</a>.","ieee":"L. Faisant, “Motivic distribution of rational curves and twisted products of toric varieties,” <i>Algebra &#38; Number Theory</i>, vol. 19. Mathematical Sciences Publishers, pp. 883–965, 2025.","short":"L. Faisant, Algebra &#38; Number Theory 19 (2025) 883–965.","ista":"Faisant L. 2025. Motivic distribution of rational curves and twisted products of toric varieties. Algebra &#38; Number Theory. 19, 883–965.","ama":"Faisant L. Motivic distribution of rational curves and twisted products of toric varieties. <i>Algebra &#38; Number Theory</i>. 2025;19:883-965. doi:<a href=\"https://doi.org/10.2140/ant.2025.19.883\">10.2140/ant.2025.19.883</a>"},"PlanS_conform":"1","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"author":[{"first_name":"Loïs","last_name":"Faisant","id":"26ca6926-5797-11ee-9232-f8b51bd19631","full_name":"Faisant, Loïs"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_place":"publisher","volume":19,"article_processing_charge":"No","page":"883-965","publication_status":"published","external_id":{"arxiv":["2302.07339"]},"abstract":[{"lang":"eng","text":"This work concerns asymptotical stabilisation phenomena occurring in the moduli space of sections of certain algebraic families over a smooth projective curve, whenever the generic fibre of the family is a smooth projective Fano variety, or not far from being Fano.\r\n We describe the expected behaviour of the class, in a ring of motivic integration, of the moduli space of sections of given numerical class. Up to an adequate normalisation, it should converge, when the class of the sections goes arbitrarily far from the boundary of the dual of the effective cone, to an effective element given by a motivic Euler product. Such a principle can be seen as an analogue for rational curves of the Batyrev-Manin-Peyre principle for rational points.\r\n The central tool of this article is the property of equidistribution of curves. We show that this notion does not depend on the choice of a model of the generic fibre, and that equidistribution of curves holds for smooth projective split toric varieties. As an application, we study the Batyrev-Manin-Peyre principle for curves on a certain kind of twisted products."}],"title":"Motivic distribution of rational curves and twisted products of toric varieties","date_created":"2025-02-18T13:33:14Z","year":"2025","researchdata_availability":"no","doi":"10.2140/ant.2025.19.883","publication_identifier":{"eissn":["1944-7833"]},"das_tickbox":"0","publication":"Algebra & Number Theory","supplementarymaterial":"no","corr_author":"1","file":[{"success":1,"creator":"dernst","file_name":"2025_AlgebraNumberTheory_Faisant.pdf","content_type":"application/pdf","date_created":"2026-02-17T13:17:00Z","file_size":2034433,"date_updated":"2026-02-17T13:17:00Z","access_level":"open_access","checksum":"56299f55682528a7cd0136497ce8b383","relation":"main_file","file_id":"21307"}],"quality_controlled":"1","has_accepted_license":"1","ddc":["510"]},{"oa":1,"file_date_updated":"2025-12-30T08:05:42Z","isi":1,"department":[{"_id":"TiBr"}],"publisher":"Elsevier","date_updated":"2026-07-16T09:26:47Z","month":"08","language":[{"iso":"eng"}],"date_published":"2025-08-01T00:00:00Z","type":"journal_article","article_type":"original","intvolume":"       273","oa_version":"Published Version","_id":"19363","scopus_import":"1","PlanS_conform":"1","citation":{"ieee":"S. Chan, P. Koymans, C. Pagano, and E. Sofos, “Averages of multiplicative functions along equidistributed sequences,” <i>Journal of Number Theory</i>, vol. 273. Elsevier, pp. 1–36, 2025.","short":"S. Chan, P. Koymans, C. Pagano, E. Sofos, Journal of Number Theory 273 (2025) 1–36.","ista":"Chan S, Koymans P, Pagano C, Sofos E. 2025. Averages of multiplicative functions along equidistributed sequences. Journal of Number Theory. 273, 1–36.","ama":"Chan S, Koymans P, Pagano C, Sofos E. Averages of multiplicative functions along equidistributed sequences. <i>Journal of Number Theory</i>. 2025;273:1-36. doi:<a href=\"https://doi.org/10.1016/j.jnt.2025.01.005\">10.1016/j.jnt.2025.01.005</a>","apa":"Chan, S., Koymans, P., Pagano, C., &#38; Sofos, E. (2025). Averages of multiplicative functions along equidistributed sequences. <i>Journal of Number Theory</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jnt.2025.01.005\">https://doi.org/10.1016/j.jnt.2025.01.005</a>","chicago":"Chan, Stephanie, Peter Koymans, Carlo Pagano, and Efthymios Sofos. “Averages of Multiplicative Functions along Equidistributed Sequences.” <i>Journal of Number Theory</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.jnt.2025.01.005\">https://doi.org/10.1016/j.jnt.2025.01.005</a>.","mla":"Chan, Stephanie, et al. “Averages of Multiplicative Functions along Equidistributed Sequences.” <i>Journal of Number Theory</i>, vol. 273, Elsevier, 2025, pp. 1–36, doi:<a href=\"https://doi.org/10.1016/j.jnt.2025.01.005\">10.1016/j.jnt.2025.01.005</a>."},"OA_type":"hybrid","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","status":"public","abstract":[{"text":"For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.","lang":"eng"}],"publication_status":"published","external_id":{"isi":["001444208500001"]},"page":"1-36","article_processing_charge":"Yes (in subscription journal)","title":"Averages of multiplicative functions along equidistributed sequences","OA_place":"publisher","volume":273,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"first_name":"Yik Tung","last_name":"Chan","full_name":"Chan, Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","orcid":"0000-0001-8467-4106"},{"last_name":"Koymans","first_name":"Peter","full_name":"Koymans, Peter"},{"full_name":"Pagano, Carlo","first_name":"Carlo","last_name":"Pagano"},{"full_name":"Sofos, Efthymios","last_name":"Sofos","first_name":"Efthymios"}],"file":[{"date_created":"2025-12-30T08:05:42Z","file_name":"2025_JourNumberTheory_Chan.pdf","content_type":"application/pdf","creator":"dernst","success":1,"file_id":"20889","relation":"main_file","checksum":"752c407eb186d391380b10a7505f66cf","access_level":"open_access","date_updated":"2025-12-30T08:05:42Z","file_size":685204}],"quality_controlled":"1","corr_author":"1","supplementarymaterial":"no","ddc":["510"],"has_accepted_license":"1","researchdata_availability":"no","year":"2025","date_created":"2025-03-09T23:01:26Z","publication":"Journal of Number Theory","das_tickbox":"1","publication_identifier":{"issn":["0022-314X"]},"doi":"10.1016/j.jnt.2025.01.005","dataavailabilitystatement":"No data was used for the research described in the article."},{"_id":"19055","acknowledgement":"The author acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034413.\r\n","type":"preprint","oa_version":"Preprint","department":[{"_id":"TiBr"}],"arxiv":1,"date_updated":"2026-07-16T09:24:48Z","language":[{"iso":"eng"}],"month":"02","date_published":"2025-02-17T00:00:00Z","oa":1,"day":"17","status":"public","OA_type":"green","ec_funded":1,"project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program"}],"citation":{"chicago":"Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2502.11704\">https://doi.org/10.48550/ARXIV.2502.11704</a>.","apa":"Faisant, L. (n.d.). Motivic counting of rational curves with tangency conditions via universal torsors. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2502.11704\">https://doi.org/10.48550/ARXIV.2502.11704</a>","mla":"Faisant, Loïs. “Motivic Counting of Rational Curves with Tangency Conditions via Universal Torsors.” <i>ArXiv</i>, 2502.11704, doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.11704\">10.48550/ARXIV.2502.11704</a>.","ieee":"L. Faisant, “Motivic counting of rational curves with tangency conditions via universal torsors,” <i>arXiv</i>. .","short":"L. Faisant, ArXiv (n.d.).","ista":"Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. arXiv, 2502.11704.","ama":"Faisant L. Motivic counting of rational curves with tangency conditions via universal torsors. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2502.11704\">10.48550/ARXIV.2502.11704</a>"},"OA_place":"repository","author":[{"last_name":"Faisant","first_name":"Loïs","id":"26ca6926-5797-11ee-9232-f8b51bd19631","full_name":"Faisant, Loïs"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Motivic counting of rational curves with tangency conditions via universal torsors","abstract":[{"lang":"eng","text":"Using the formalism of Cox rings and universal torsors, we prove a decomposition of the Grothendieck motive of the moduli space of morphisms from an arbitrary smooth projective curve to a Mori Dream Space (MDS).\r\n For the simplest cases of MDS, that of toric varieties, we use this decomposition to prove an instance of the motivic Batyrev--Manin--Peyre principle for curves satisfying tangency conditions with respect to the boundary divisors, often called Campana curves."}],"external_id":{"arxiv":["2502.11704"]},"publication_status":"submitted","article_processing_charge":"No","publication":"arXiv","das_tickbox":"0","doi":"10.48550/ARXIV.2502.11704","researchdata_availability":"no","article_number":"2502.11704","year":"2025","date_created":"2025-02-18T13:34:07Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2502.11704","open_access":"1"}],"corr_author":"1","supplementarymaterial":"no"}]