[{"publisher":"Oxford University Press","article_type":"original","oa_version":"Published Version","ddc":["500"],"date_updated":"2026-10-14T08:49:05Z","PlanS_conform":"1","date_created":"2026-10-12T13:58:16Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1093/qmath/haag037","project":[{"_id":"bd8a4fdc-d553-11ed-ba76-80a0167441a3","name":"Rational curves via function field analytic number theory","grant_number":"P36278"}],"article_number":"haag037","department":[{"_id":"TiBr"}],"OA_type":"hybrid","article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"},{"first_name":"Will","last_name":"Sawin","full_name":"Sawin, Will"}],"scopus_import":"1","oa":1,"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","publication_status":"epub_ahead","quality_controlled":"1","das_tickbox":"0","publication":"The Quarterly Journal of Mathematics","day":"06","citation":{"ieee":"T. D. Browning and W. Sawin, “Random diophantine equations of large degree,” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2026.","ama":"Browning TD, Sawin W. Random diophantine equations of large degree. <i>The Quarterly Journal of Mathematics</i>. 2026. doi:<a href=\"https://doi.org/10.1093/qmath/haag037\">10.1093/qmath/haag037</a>","apa":"Browning, T. D., &#38; Sawin, W. (2026). Random diophantine equations of large degree. <i>The Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haag037\">https://doi.org/10.1093/qmath/haag037</a>","chicago":"Browning, Timothy D, and Will Sawin. “Random Diophantine Equations of Large Degree.” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2026. <a href=\"https://doi.org/10.1093/qmath/haag037\">https://doi.org/10.1093/qmath/haag037</a>.","mla":"Browning, Timothy D., and Will Sawin. “Random Diophantine Equations of Large Degree.” <i>The Quarterly Journal of Mathematics</i>, haag037, Oxford University Press, 2026, doi:<a href=\"https://doi.org/10.1093/qmath/haag037\">10.1093/qmath/haag037</a>.","short":"T.D. Browning, W. Sawin, The Quarterly Journal of Mathematics (2026).","ista":"Browning TD, Sawin W. 2026. Random diophantine equations of large degree. The Quarterly Journal of Mathematics., haag037."},"_id":"23124","supplementarymaterial":"no","OA_place":"publisher","acknowledgement":"The authors are very grateful to Pierre Le Boudec, whose contributions would have merited coauthorship. At his request, however, he is not listed as a co-author, since he has chosen to pursue\r\na career outside academia. T.B. was supported by a grant from the IAS School of Mathematics\r\nand a FWF grant (DOI 10.55776/P36278). W.S. was supported by NSF grant DMS-2502029 and\r\na Sloan Research Fellowship.","corr_author":"1","title":"Random diophantine equations of large degree","status":"public","license":"https://creativecommons.org/licenses/by/4.0/","year":"2026","abstract":[{"text":"Among the set of hypersurfaces of degree d and dimension  defined by the vanishing\r\nof a homogeneous polynomial with coefficients in the set {−1, +1}, we investigate the\r\nprobability that a hypersurface contains a rational point as d and  tend to ∞.","lang":"eng"}],"month":"10","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1093/qmath/haag037"}],"publication_identifier":{"issn":["0033-5606"],"eissn":["1464-3847"]},"researchdata_availability":"no","external_id":{"arxiv":["2510.26191"]},"arxiv":1,"doi":"10.1093/qmath/haag037","date_published":"2026-10-06T00:00:00Z"},{"status":"public","title":"Exponentially many graphs are determined by their spectrum","corr_author":"1","abstract":[{"lang":"eng","text":"As a discrete analogue of Kac’s celebrated question on ‘hearing the shape of a drum’ and towards a practical\r\ngraph isomorphism test, it is of interest to understand which graphs are determined up to isomorphism by\r\ntheir spectrum (of their adjacency matrix). A striking conjecture in this area, due to van Dam and Haemers,\r\nis that ‘almost all graphs are determined by their spectrum’, meaning that the fraction of unlabelled n-vertex\r\ngraphs which are determined by their spectrum converges to 1 as n → ∞.\r\nIn this paper, we make a step towards this conjecture, showing that there are exponentially many n-vertex\r\ngraphs which are determined by their spectrum. This improves on previous bounds (of shape e\r\nc\r\n√\r\nn\r\n). We also\r\npropose a number of further directions of research.\r\n"}],"year":"2024","supplementarymaterial":"no","acknowledgement":"Matthew Kwan was supported by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777.","citation":{"ista":"Koval I, Kwan MA. 2024. Exponentially many graphs are determined by their spectrum. Quarterly Journal of Mathematics. 75(3), 869–899.","short":"I. Koval, M.A. Kwan, Quarterly Journal of Mathematics 75 (2024) 869–899.","chicago":"Koval, Illya, and Matthew Alan Kwan. “Exponentially Many Graphs Are Determined by Their Spectrum.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/qmath/haae030\">https://doi.org/10.1093/qmath/haae030</a>.","mla":"Koval, Illya, and Matthew Alan Kwan. “Exponentially Many Graphs Are Determined by Their Spectrum.” <i>Quarterly Journal of Mathematics</i>, vol. 75, no. 3, Oxford University Press, 2024, pp. 869–99, doi:<a href=\"https://doi.org/10.1093/qmath/haae030\">10.1093/qmath/haae030</a>.","apa":"Koval, I., &#38; Kwan, M. A. (2024). Exponentially many graphs are determined by their spectrum. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haae030\">https://doi.org/10.1093/qmath/haae030</a>","ama":"Koval I, Kwan MA. Exponentially many graphs are determined by their spectrum. <i>Quarterly Journal of Mathematics</i>. 2024;75(3):869-899. doi:<a href=\"https://doi.org/10.1093/qmath/haae030\">10.1093/qmath/haae030</a>","ieee":"I. Koval and M. A. Kwan, “Exponentially many graphs are determined by their spectrum,” <i>Quarterly Journal of Mathematics</i>, vol. 75, no. 3. Oxford University Press, pp. 869–899, 2024."},"day":"19","quality_controlled":"1","publication":"Quarterly Journal of Mathematics","das_tickbox":"0","_id":"17475","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"checksum":"abf200d37ad69e6f2c0750a30296ad97","relation":"main_file","file_name":"2024_QuJofMath_Koval.pdf","file_id":"17851","success":1,"date_updated":"2024-09-06T12:23:57Z","file_size":946411,"creator":"cchlebak","content_type":"application/pdf","date_created":"2024-09-06T12:23:57Z","access_level":"open_access"}],"publication_status":"published","has_accepted_license":"1","arxiv":1,"doi":"10.1093/qmath/haae030","date_published":"2024-06-19T00:00:00Z","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"researchdata_availability":"no","external_id":{"isi":["001249741500001"],"arxiv":["2309.09788"]},"page":"869-899","type":"journal_article","isi":1,"month":"06","date_created":"2024-09-01T22:01:07Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_updated":"2026-10-16T10:14:59Z","volume":75,"file_date_updated":"2024-09-06T12:23:57Z","ddc":["500"],"publisher":"Oxford University Press","oa_version":"Published Version","article_type":"original","article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Koval, Illya","last_name":"Koval","first_name":"Illya","id":"2eed1f3b-896a-11ed-bdf8-93c7c4bf159e"},{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan","full_name":"Kwan, Matthew Alan"}],"department":[{"_id":"MaKw"},{"_id":"VaKa"}],"scopus_import":"1","oa":1,"fulldoi":"https://doi.org/10.1093/qmath/haae030","project":[{"grant_number":"101076777","name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"issue":"3","intvolume":"        75","language":[{"iso":"eng"}]},{"isi":1,"month":"12","page":"1243-1254","type":"journal_article","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"researchdata_availability":"no","external_id":{"isi":["001304396600001"]},"date_published":"2024-12-01T00:00:00Z","doi":"10.1093/qmath/haae044","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"date_created":"2025-01-28T07:03:51Z","access_level":"open_access","content_type":"application/pdf","creator":"dernst","date_updated":"2025-01-28T07:03:51Z","file_size":424645,"file_id":"18931","success":1,"file_name":"2024_QuarterlyJourMath_Elsholtz.pdf","checksum":"1a06e052761d3f1e873463d6f529dd82","relation":"main_file"}],"publication_status":"published","has_accepted_license":"1","citation":{"ista":"Elsholtz C, Wurzinger L. 2024. Sumsets in the set of squares. The Quarterly Journal of Mathematics. 75(4), 1243–1254.","short":"C. Elsholtz, L. Wurzinger, The Quarterly Journal of Mathematics 75 (2024) 1243–1254.","mla":"Elsholtz, Christian, and Lena Wurzinger. “Sumsets in the Set of Squares.” <i>The Quarterly Journal of Mathematics</i>, vol. 75, no. 4, Oxford University Press, 2024, pp. 1243–54, doi:<a href=\"https://doi.org/10.1093/qmath/haae044\">10.1093/qmath/haae044</a>.","chicago":"Elsholtz, Christian, and Lena Wurzinger. “Sumsets in the Set of Squares.” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/qmath/haae044\">https://doi.org/10.1093/qmath/haae044</a>.","apa":"Elsholtz, C., &#38; Wurzinger, L. (2024). Sumsets in the set of squares. <i>The Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haae044\">https://doi.org/10.1093/qmath/haae044</a>","ama":"Elsholtz C, Wurzinger L. Sumsets in the set of squares. <i>The Quarterly Journal of Mathematics</i>. 2024;75(4):1243-1254. doi:<a href=\"https://doi.org/10.1093/qmath/haae044\">10.1093/qmath/haae044</a>","ieee":"C. Elsholtz and L. Wurzinger, “Sumsets in the set of squares,” <i>The Quarterly Journal of Mathematics</i>, vol. 75, no. 4. Oxford University Press, pp. 1243–1254, 2024."},"day":"01","publication":"The Quarterly Journal of Mathematics","das_tickbox":"0","quality_controlled":"1","_id":"18930","supplementarymaterial":"no","OA_place":"publisher","acknowledgement":"This manuscript grew out of the second author’s MSc Thesis at Graz University of Technology [34]. C. Elsholtz is supported by a joint FWF-ANR project ArithRand, grant numbers FWF I 4945-N and ANR-20-CE91-0006. Both authors would like to thank Igor Shparlinski for drawing our attention to related character sum estimates. Furthermore, we would like to thank the referee for a careful reading of the paper.","title":"Sumsets in the set of squares","status":"public","corr_author":"1","abstract":[{"lang":"eng","text":"We study sumsets 𝒜 + ℬ in the set of squares 𝒮 (and, more generally, in the set of kth powers 𝒮k, where k ≥2 is an integer). It is known by a result of Gyarmati that 𝒜 + ℬ ⊂ 𝒮k ∩[1,N] implies that min(|𝒜|,|ℬ|) =Ok(logN). Here, we study how the upper bound on |ℬ| decreases, when the size of |𝒜| increases (or vice versa). In particular, if |𝒜| ≥ Ck1m m(logN)1m , then |ℬ| = Ok(m2logN), for sufficiently large N, a positive integer m and an explicit constant C > 0. For example, with m ∼ loglogN this gives: If |𝒜| ≥ CkloglogN,then |ℬ| = Ok(logN(loglogN)2)."}],"year":"2024","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1093/qmath/haae044","intvolume":"        75","issue":"4","author":[{"full_name":"Elsholtz, Christian","last_name":"Elsholtz","first_name":"Christian"},{"last_name":"Wurzinger","full_name":"Wurzinger, Lena","id":"50c57d72-32a8-11ee-aeea-d652094d2ccd","first_name":"Lena","orcid":"0009-0004-5360-0074"}],"OA_type":"hybrid","department":[{"_id":"TiBr"}],"article_processing_charge":"Yes (via OA deal)","oa":1,"scopus_import":"1","publisher":"Oxford University Press","oa_version":"Published Version","article_type":"original","volume":75,"ddc":["510"],"file_date_updated":"2025-01-28T07:03:51Z","date_updated":"2026-10-21T11:06:48Z","PlanS_conform":"1","date_created":"2025-01-28T06:55:31Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"publisher":"Oxford University Press","article_type":"original","oa_version":"Preprint","volume":74,"date_updated":"2026-07-14T10:55:52Z","extern":"1","date_created":"2026-06-29T12:56:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1093/qmath/haad030","issue":"4","intvolume":"        74","author":[{"first_name":"Vivian Zieve","id":"c3bac823-112d-11f0-a3f5-c264f852e697","full_name":"Kuperberg, Vivian Zieve","last_name":"Kuperberg"}],"OA_type":"green","article_processing_charge":"No","scopus_import":"1","oa":1,"publication_status":"published","quality_controlled":"1","publication":"The Quarterly Journal of Mathematics","day":"01","citation":{"ieee":"V. Z. Kuperberg, “Sums of singular series with large sets and the tail of the distribution of primes,” <i>The Quarterly Journal of Mathematics</i>, vol. 74, no. 4. Oxford University Press, pp. 1457–1479, 2023.","ama":"Kuperberg VZ. Sums of singular series with large sets and the tail of the distribution of primes. <i>The Quarterly Journal of Mathematics</i>. 2023;74(4):1457-1479. doi:<a href=\"https://doi.org/10.1093/qmath/haad030\">10.1093/qmath/haad030</a>","apa":"Kuperberg, V. Z. (2023). Sums of singular series with large sets and the tail of the distribution of primes. <i>The Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haad030\">https://doi.org/10.1093/qmath/haad030</a>","chicago":"Kuperberg, Vivian Zieve. “Sums of Singular Series with Large Sets and the Tail of the Distribution of Primes.” <i>The Quarterly Journal of Mathematics</i>. Oxford University Press, 2023. <a href=\"https://doi.org/10.1093/qmath/haad030\">https://doi.org/10.1093/qmath/haad030</a>.","mla":"Kuperberg, Vivian Zieve. “Sums of Singular Series with Large Sets and the Tail of the Distribution of Primes.” <i>The Quarterly Journal of Mathematics</i>, vol. 74, no. 4, Oxford University Press, 2023, pp. 1457–79, doi:<a href=\"https://doi.org/10.1093/qmath/haad030\">10.1093/qmath/haad030</a>.","short":"V.Z. Kuperberg, The Quarterly Journal of Mathematics 74 (2023) 1457–1479.","ista":"Kuperberg VZ. 2023. Sums of singular series with large sets and the tail of the distribution of primes. The Quarterly Journal of Mathematics. 74(4), 1457–1479."},"_id":"22192","OA_place":"repository","status":"public","title":"Sums of singular series with large sets and the tail of the distribution of primes","abstract":[{"lang":"eng","text":"In 1976, Gallagher showed that the Hardy–Littlewood conjectures on prime k-tuples imply that the\r\ndistribution of primes in log-size intervals is Poissonian. He did so by computing average values\r\nof the singular series constants over different sets of a fixed size k contained in an interval [1,h]\r\nas h → ∞, and then using this average to compute moments of the distribution of primes. In this\r\npaper, we study averages where k is relatively large with respect to h. We then apply these averages\r\nto the tail of the distribution. For example, we show, assuming appropriate Hardy–Littlewood\r\nconjectures and in certain ranges of the parameters, the number of intervals [n,n + λlogx] with\r\nn ≤ x containing at least k primes is ≪ x exp(−k/(λe))."}],"year":"2023","month":"12","page":"1457-1479","type":"journal_article","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.09775","open_access":"1"}],"publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"external_id":{"arxiv":["2210.09775"]},"arxiv":1,"date_published":"2023-12-01T00:00:00Z","doi":"10.1093/qmath/haad030"},{"date_updated":"2026-07-29T10:22:09Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2023-12-31T23:01:03Z","oa_version":"Published Version","article_type":"original","publisher":"Oxford University Press","file_date_updated":"2024-01-02T07:37:09Z","ddc":["510"],"volume":74,"oa":1,"scopus_import":"1","author":[{"first_name":"Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","full_name":"Horesh, Tal","last_name":"Horesh"},{"last_name":"Karasik","full_name":"Karasik, Yakov","first_name":"Yakov"}],"department":[{"_id":"TiBr"}],"article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"intvolume":"        74","issue":"4","project":[{"name":"Between rational and integral points","_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2"}],"fulldoi":"https://doi.org/10.1093/qmath/haad008","acknowledgement":"This work was done when both authors were visiting Institute of Science and Technology (IST) Austria. T.H. was being supported by Engineering and Physical Sciences Research Council grant EP/P026710/1. Y.K. had a great time there and is grateful for the hospitality. The appendix to this paper is largely based on a mini course T.H. had given at IST in February 2020.","supplementarymaterial":"no","abstract":[{"lang":"eng","text":"We count primitive lattices of rank d inside Zn as their covolume tends to infinity, with respect to certain parameters of such lattices. These parameters include, for example, the subspace that a lattice spans, namely its projection to the Grassmannian; its homothety class and its equivalence class modulo rescaling and rotation, often referred to as a shape. We add to a prior work of Schmidt by allowing sets in the spaces of parameters that are general enough to conclude the joint equidistribution of these parameters. In addition to the primitive d-lattices Λ themselves, we also consider their orthogonal complements in Zn⁠, A1⁠, and show that the equidistribution occurs jointly for Λ and A1⁠. Finally, our asymptotic formulas for the number of primitive lattices include an explicit bound on the error term."}],"year":"2023","status":"public","title":"Equidistribution of primitive lattices in ℝn","corr_author":"1","has_accepted_license":"1","publication_status":"published","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"file_name":"2023_QuarterlyJourMath_Horesh.pdf","success":1,"file_id":"14720","relation":"main_file","checksum":"bf29baa9eae8500f3374dbcb80712687","content_type":"application/pdf","creator":"dernst","access_level":"open_access","date_created":"2024-01-02T07:37:09Z","file_size":724748,"date_updated":"2024-01-02T07:37:09Z"}],"_id":"14717","citation":{"ieee":"T. Horesh and Y. Karasik, “Equidistribution of primitive lattices in ℝn,” <i>Quarterly Journal of Mathematics</i>, vol. 74, no. 4. Oxford University Press, pp. 1253–1294, 2023.","ama":"Horesh T, Karasik Y. Equidistribution of primitive lattices in ℝn. <i>Quarterly Journal of Mathematics</i>. 2023;74(4):1253-1294. doi:<a href=\"https://doi.org/10.1093/qmath/haad008\">10.1093/qmath/haad008</a>","apa":"Horesh, T., &#38; Karasik, Y. (2023). Equidistribution of primitive lattices in ℝn. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haad008\">https://doi.org/10.1093/qmath/haad008</a>","mla":"Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in ℝn.” <i>Quarterly Journal of Mathematics</i>, vol. 74, no. 4, Oxford University Press, 2023, pp. 1253–94, doi:<a href=\"https://doi.org/10.1093/qmath/haad008\">10.1093/qmath/haad008</a>.","chicago":"Horesh, Tal, and Yakov Karasik. “Equidistribution of Primitive Lattices in ℝn.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2023. <a href=\"https://doi.org/10.1093/qmath/haad008\">https://doi.org/10.1093/qmath/haad008</a>.","ista":"Horesh T, Karasik Y. 2023. Equidistribution of primitive lattices in ℝn. Quarterly Journal of Mathematics. 74(4), 1253–1294.","short":"T. Horesh, Y. Karasik, Quarterly Journal of Mathematics 74 (2023) 1253–1294."},"day":"01","das_tickbox":"0","quality_controlled":"1","publication":"Quarterly Journal of Mathematics","external_id":{"isi":["001005945400001"],"arxiv":["2012.04508"]},"publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"researchdata_availability":"no","date_published":"2023-12-01T00:00:00Z","doi":"10.1093/qmath/haad008","arxiv":1,"isi":1,"month":"12","type":"journal_article","page":"1253-1294"},{"volume":68,"oa_version":"Submitted Version","publisher":"Oxford University Press","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2018-12-11T11:47:55Z","date_updated":"2025-09-10T14:15:30Z","issue":"2","intvolume":"        68","fulldoi":"https://doi.org/10.1093/qmath/haw053","project":[{"name":"Arithmetic and physics of Higgs moduli spaces","call_identifier":"FP7","_id":"25E549F4-B435-11E9-9278-68D0E5697425","grant_number":"320593"}],"language":[{"iso":"eng"}],"scopus_import":"1","oa":1,"article_processing_charge":"No","department":[{"_id":"TaHa"}],"author":[{"full_name":"Davison, Ben","last_name":"Davison","first_name":"Ben","id":"4634AB1E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8944-4390"}],"_id":"687","quality_controlled":"1","publication":"Quarterly Journal of Mathematics","citation":{"chicago":"Davison, Ben. “The Critical CoHA of a Quiver with Potential.” <i>Quarterly Journal of Mathematics</i>. Oxford University Press, 2017. <a href=\"https://doi.org/10.1093/qmath/haw053\">https://doi.org/10.1093/qmath/haw053</a>.","mla":"Davison, Ben. “The Critical CoHA of a Quiver with Potential.” <i>Quarterly Journal of Mathematics</i>, vol. 68, no. 2, Oxford University Press, 2017, pp. 635–703, doi:<a href=\"https://doi.org/10.1093/qmath/haw053\">10.1093/qmath/haw053</a>.","ista":"Davison B. 2017. The critical CoHA of a quiver with potential. Quarterly Journal of Mathematics. 68(2), 635–703.","short":"B. Davison, Quarterly Journal of Mathematics 68 (2017) 635–703.","ama":"Davison B. The critical CoHA of a quiver with potential. <i>Quarterly Journal of Mathematics</i>. 2017;68(2):635-703. doi:<a href=\"https://doi.org/10.1093/qmath/haw053\">10.1093/qmath/haw053</a>","ieee":"B. Davison, “The critical CoHA of a quiver with potential,” <i>Quarterly Journal of Mathematics</i>, vol. 68, no. 2. Oxford University Press, pp. 635–703, 2017.","apa":"Davison, B. (2017). The critical CoHA of a quiver with potential. <i>Quarterly Journal of Mathematics</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/qmath/haw053\">https://doi.org/10.1093/qmath/haw053</a>"},"day":"01","publication_status":"published","year":"2017","abstract":[{"lang":"eng","text":"Pursuing the similarity between the Kontsevich-Soibelman construction of the cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the integrality conjecture for motivic Donaldson-Thomas invariants and the PBW theorem for quantum enveloping algebras, we build a coproduct on the CoHA associated to a quiver with potential. We also prove a cohomological dimensional reduction theorem, further linking a special class of CoHAs with Yangians, and explaining how to connect the study of character varieties with the study of CoHAs."}],"corr_author":"1","title":"The critical CoHA of a quiver with potential","status":"public","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/1311.7172","open_access":"1"}],"page":"635 - 703","ec_funded":1,"publist_id":"7022","month":"06","isi":1,"doi":"10.1093/qmath/haw053","date_published":"2017-06-01T00:00:00Z","arxiv":1,"external_id":{"arxiv":["1311.7172"],"isi":["000404545300015"]},"publication_identifier":{"issn":["0033-5606"]}},{"publist_id":"7706","month":"03","type":"journal_article","page":"33 - 39","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"date_published":"2003-03-01T00:00:00Z","doi":"10.1093/qjmath/54.1.33","publication_status":"published","_id":"206","citation":{"mla":"Browning, Timothy D. “A Note on the Distribution of Rational Points on Threefolds.” <i>Quarterly Journal of Mathematics</i>, vol. 54, no. 1, Unknown, 2003, pp. 33–39, doi:<a href=\"https://doi.org/10.1093/qjmath/54.1.33\">10.1093/qjmath/54.1.33</a>.","chicago":"Browning, Timothy D. “A Note on the Distribution of Rational Points on Threefolds.” <i>Quarterly Journal of Mathematics</i>. Unknown, 2003. <a href=\"https://doi.org/10.1093/qjmath/54.1.33\">https://doi.org/10.1093/qjmath/54.1.33</a>.","short":"T.D. Browning, Quarterly Journal of Mathematics 54 (2003) 33–39.","ista":"Browning TD. 2003. A note on the distribution of rational points on threefolds. Quarterly Journal of Mathematics. 54(1), 33–39.","ama":"Browning TD. A note on the distribution of rational points on threefolds. <i>Quarterly Journal of Mathematics</i>. 2003;54(1):33-39. doi:<a href=\"https://doi.org/10.1093/qjmath/54.1.33\">10.1093/qjmath/54.1.33</a>","ieee":"T. D. Browning, “A note on the distribution of rational points on threefolds,” <i>Quarterly Journal of Mathematics</i>, vol. 54, no. 1. Unknown, pp. 33–39, 2003.","apa":"Browning, T. D. (2003). A note on the distribution of rational points on threefolds. <i>Quarterly Journal of Mathematics</i>. Unknown. <a href=\"https://doi.org/10.1093/qjmath/54.1.33\">https://doi.org/10.1093/qjmath/54.1.33</a>"},"day":"01","quality_controlled":"1","publication":"Quarterly Journal of Mathematics","abstract":[{"lang":"eng","text":"Let T ⊂ ℙ 4 be a non-singular threefold of degree at least four. Then we show that the number of points in T(ℚ), with height at most B, is o(B 3) or B → ∞."}],"year":"2003","title":"A note on the distribution of rational points on threefolds","status":"public","language":[{"iso":"eng"}],"intvolume":"        54","issue":"1","fulldoi":"https://doi.org/10.1093/qjmath/54.1.33","scopus_import":"1","author":[{"first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D","last_name":"Browning"}],"article_processing_charge":"No","OA_type":"closed access","oa_version":"None","article_type":"original","publisher":"Unknown","volume":54,"date_updated":"2026-05-29T07:14:27Z","extern":"1","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_created":"2018-12-11T11:45:12Z"},{"OA_type":"closed access","author":[{"full_name":"Browning, Timothy D","last_name":"Browning","orcid":"0000-0002-8314-0177","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","scopus_import":"1","fulldoi":"https://doi.org/doi/10.1093/qjmath/54.1.11","intvolume":"        54","issue":"1","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:45:13Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","extern":"1","date_updated":"2026-05-29T07:10:52Z","volume":54,"publisher":"Oxford Academic","article_type":"original","oa_version":"None","date_published":"2003-03-01T00:00:00Z","doi":"doi/10.1093/qjmath/54.1.11","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"page":"11 - 31","type":"journal_article","publist_id":"7705","month":"03","status":"public","title":"Counting rational points on diagonal quadratic surfaces","year":"2003","abstract":[{"text":"For any ε > 0 and any diagonal quadratic form Q ∈ Z[x1, x2, x3, x4] with a square‐free discriminant of modulus ΔQ ≠ 0, we establish the uniform estimate ≪ε B3/2+ε + B2+ε/Δ1/6Q for the number of rational points of height at most B lying in the projective surface Q = 0.\r\n\r\n","lang":"eng"}],"quality_controlled":"1","publication":"Quarterly Journal of Mathematics","citation":{"ista":"Browning TD. 2003. Counting rational points on diagonal quadratic surfaces. Quarterly Journal of Mathematics. 54(1), 11–31.","short":"T.D. Browning, Quarterly Journal of Mathematics 54 (2003) 11–31.","mla":"Browning, Timothy D. “Counting Rational Points on Diagonal Quadratic Surfaces.” <i>Quarterly Journal of Mathematics</i>, vol. 54, no. 1, Oxford Academic, 2003, pp. 11–31, doi:<a href=\"https://doi.org/doi/10.1093/qjmath/54.1.11\">doi/10.1093/qjmath/54.1.11</a>.","chicago":"Browning, Timothy D. “Counting Rational Points on Diagonal Quadratic Surfaces.” <i>Quarterly Journal of Mathematics</i>. Oxford Academic, 2003. <a href=\"https://doi.org/doi/10.1093/qjmath/54.1.11\">https://doi.org/doi/10.1093/qjmath/54.1.11</a>.","apa":"Browning, T. D. (2003). Counting rational points on diagonal quadratic surfaces. <i>Quarterly Journal of Mathematics</i>. Oxford Academic. <a href=\"https://doi.org/doi/10.1093/qjmath/54.1.11\">https://doi.org/doi/10.1093/qjmath/54.1.11</a>","ama":"Browning TD. Counting rational points on diagonal quadratic surfaces. <i>Quarterly Journal of Mathematics</i>. 2003;54(1):11-31. doi:<a href=\"https://doi.org/doi/10.1093/qjmath/54.1.11\">doi/10.1093/qjmath/54.1.11</a>","ieee":"T. D. Browning, “Counting rational points on diagonal quadratic surfaces,” <i>Quarterly Journal of Mathematics</i>, vol. 54, no. 1. Oxford Academic, pp. 11–31, 2003."},"day":"01","_id":"208","publication_status":"published"}]