[{"publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"_id":"17475","has_accepted_license":"1","day":"19","quality_controlled":"1","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1093/qmath/haae030","file":[{"file_name":"2024_QuJofMath_Koval.pdf","creator":"cchlebak","relation":"main_file","access_level":"open_access","date_updated":"2024-09-06T12:23:57Z","date_created":"2024-09-06T12:23:57Z","content_type":"application/pdf","file_id":"17851","file_size":946411,"checksum":"abf200d37ad69e6f2c0750a30296ad97","success":1}],"external_id":{"isi":["001249741500001"],"arxiv":["2309.09788"]},"citation":{"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.","short":"I. Koval, M.A. Kwan, Quarterly Journal of Mathematics 75 (2024) 869–899.","ista":"Koval I, Kwan MA. 2024. Exponentially many graphs are determined by their spectrum. Quarterly Journal of Mathematics. 75(3), 869–899.","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>","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>."},"date_created":"2024-09-01T22:01:07Z","corr_author":"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"},"volume":75,"page":"869-899","department":[{"_id":"MaKw"},{"_id":"VaKa"}],"type":"journal_article","article_processing_charge":"Yes (via OA deal)","acknowledgement":"Matthew Kwan was supported by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777.","publication":"Quarterly Journal of Mathematics","year":"2024","isi":1,"abstract":[{"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","lang":"eng"}],"oa_version":"Published Version","article_type":"original","ddc":["500"],"file_date_updated":"2024-09-06T12:23:57Z","date_updated":"2025-09-08T09:09:41Z","status":"public","oa":1,"scopus_import":"1","title":"Exponentially many graphs are determined by their spectrum","month":"06","author":[{"last_name":"Koval","full_name":"Koval, Illya","first_name":"Illya","id":"2eed1f3b-896a-11ed-bdf8-93c7c4bf159e"},{"full_name":"Kwan, Matthew Alan","last_name":"Kwan","orcid":"0000-0002-4003-7567","first_name":"Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"}],"issue":"3","publication_status":"published","intvolume":"        75","date_published":"2024-06-19T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","grant_number":"101076777","name":"Randomness and structure in combinatorics"}],"publisher":"Oxford University Press","doi":"10.1093/qmath/haae030","arxiv":1},{"has_accepted_license":"1","day":"01","_id":"18930","PlanS_conform":"1","publication_identifier":{"issn":["0033-5606"],"eissn":["1464-3847"]},"language":[{"iso":"eng"}],"quality_controlled":"1","fulldoi":"https://doi.org/10.1093/qmath/haae044","external_id":{"isi":["001304396600001"]},"file":[{"success":1,"checksum":"1a06e052761d3f1e873463d6f529dd82","file_id":"18931","file_size":424645,"content_type":"application/pdf","date_created":"2025-01-28T07:03:51Z","date_updated":"2025-01-28T07:03:51Z","access_level":"open_access","file_name":"2024_QuarterlyJourMath_Elsholtz.pdf","relation":"main_file","creator":"dernst"}],"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"},"corr_author":"1","date_created":"2025-01-28T06:55:31Z","citation":{"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.","short":"C. Elsholtz, L. Wurzinger, The Quarterly Journal of Mathematics 75 (2024) 1243–1254.","ista":"Elsholtz C, Wurzinger L. 2024. Sumsets in the set of squares. The Quarterly Journal of Mathematics. 75(4), 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>.","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>","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>","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>."},"page":"1243-1254","volume":75,"OA_place":"publisher","type":"journal_article","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"TiBr"}],"supplementarymaterial":"no","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.","OA_type":"hybrid","das_tickbox":"0","isi":1,"year":"2024","publication":"The Quarterly Journal of Mathematics","article_type":"original","ddc":["510"],"oa_version":"Published Version","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)."}],"file_date_updated":"2025-01-28T07:03:51Z","issue":"4","author":[{"last_name":"Elsholtz","full_name":"Elsholtz, Christian","first_name":"Christian"},{"orcid":"0009-0004-5360-0074","id":"50c57d72-32a8-11ee-aeea-d652094d2ccd","first_name":"Lena","full_name":"Wurzinger, Lena","last_name":"Wurzinger"}],"scopus_import":"1","month":"12","title":"Sumsets in the set of squares","status":"public","oa":1,"date_updated":"2026-07-29T09:58:28Z","date_published":"2024-12-01T00:00:00Z","publication_status":"published","intvolume":"        75","publisher":"Oxford University Press","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","researchdata_availability":"no","doi":"10.1093/qmath/haae044"},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.09775","open_access":"1"}],"intvolume":"        74","publication_status":"published","date_published":"2023-12-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Oxford University Press","doi":"10.1093/qmath/haad030","arxiv":1,"year":"2023","publication":"The Quarterly Journal of Mathematics","oa_version":"Preprint","abstract":[{"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)).","lang":"eng"}],"article_type":"original","oa":1,"status":"public","date_updated":"2026-07-14T10:55:52Z","author":[{"full_name":"Kuperberg, Vivian Zieve","last_name":"Kuperberg","id":"c3bac823-112d-11f0-a3f5-c264f852e697","first_name":"Vivian Zieve"}],"issue":"4","month":"12","scopus_import":"1","title":"Sums of singular series with large sets and the tail of the distribution of primes","date_created":"2026-06-29T12:56:30Z","extern":"1","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.","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.","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>.","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>.","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>"},"volume":74,"OA_place":"repository","page":"1457-1479","article_processing_charge":"No","type":"journal_article","OA_type":"green","_id":"22192","publication_identifier":{"issn":["0033-5606"],"eissn":["1464-3847"]},"day":"01","language":[{"iso":"eng"}],"quality_controlled":"1","fulldoi":"https://doi.org/10.1093/qmath/haad030","external_id":{"arxiv":["2210.09775"]}},{"file":[{"date_updated":"2024-01-02T07:37:09Z","access_level":"open_access","file_name":"2023_QuarterlyJourMath_Horesh.pdf","creator":"dernst","relation":"main_file","success":1,"checksum":"bf29baa9eae8500f3374dbcb80712687","file_id":"14720","file_size":724748,"content_type":"application/pdf","date_created":"2024-01-02T07:37:09Z"}],"external_id":{"arxiv":["2012.04508"],"isi":["001005945400001"]},"fulldoi":"https://doi.org/10.1093/qmath/haad008","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0033-5606"],"eissn":["1464-3847"]},"_id":"14717","has_accepted_license":"1","day":"01","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","department":[{"_id":"TiBr"}],"type":"journal_article","article_processing_charge":"Yes (via OA deal)","volume":74,"page":"1253-1294","citation":{"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>.","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>","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>.","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>","ista":"Horesh T, Karasik Y. 2023. Equidistribution of primitive lattices in ℝn. Quarterly Journal of Mathematics. 74(4), 1253–1294.","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.","short":"T. Horesh, Y. Karasik, Quarterly Journal of Mathematics 74 (2023) 1253–1294."},"date_created":"2023-12-31T23:01:03Z","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"},"corr_author":"1","date_updated":"2026-07-29T10:22:09Z","oa":1,"status":"public","month":"12","title":"Equidistribution of primitive lattices in ℝn","scopus_import":"1","issue":"4","author":[{"last_name":"Horesh","full_name":"Horesh, Tal","id":"C8B7BF48-8D81-11E9-BCA9-F536E6697425","first_name":"Tal"},{"last_name":"Karasik","full_name":"Karasik, Yakov","first_name":"Yakov"}],"file_date_updated":"2024-01-02T07:37:09Z","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."}],"oa_version":"Published Version","article_type":"original","ddc":["510"],"publication":"Quarterly Journal of Mathematics","year":"2023","das_tickbox":"0","isi":1,"doi":"10.1093/qmath/haad008","researchdata_availability":"no","arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","project":[{"_id":"26A8D266-B435-11E9-9278-68D0E5697425","grant_number":"EP-P026710-2","name":"Between rational and integral points"}],"publisher":"Oxford University Press","intvolume":"        74","publication_status":"published","date_published":"2023-12-01T00:00:00Z"},{"type":"journal_article","article_processing_charge":"No","OA_type":"closed access","extern":"1","date_created":"2018-12-11T11:45:12Z","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>.","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>","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>","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>.","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.","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."},"page":"33 - 39","volume":54,"fulldoi":"https://doi.org/10.1093/qjmath/54.1.33","day":"01","_id":"206","publication_identifier":{"eissn":["1464-3847"],"issn":["0033-5606"]},"language":[{"iso":"eng"}],"publist_id":"7706","quality_controlled":"1","publisher":"Unknown","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.1093/qjmath/54.1.33","date_published":"2003-03-01T00:00:00Z","intvolume":"        54","publication_status":"published","author":[{"full_name":"Browning, Timothy D","last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"}],"issue":"1","title":"A note on the distribution of rational points on threefolds","scopus_import":"1","month":"03","status":"public","date_updated":"2026-05-29T07:14:27Z","year":"2003","publication":"Quarterly Journal of Mathematics","article_type":"original","oa_version":"None","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 → ∞."}]},{"page":"11 - 31","volume":54,"date_created":"2018-12-11T11:45:13Z","extern":"1","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.","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.","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>","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>","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>."},"OA_type":"closed access","article_processing_charge":"No","type":"journal_article","language":[{"iso":"eng"}],"publist_id":"7705","quality_controlled":"1","day":"01","_id":"208","publication_identifier":{"issn":["0033-5606"],"eissn":["1464-3847"]},"fulldoi":"https://doi.org/doi/10.1093/qjmath/54.1.11","date_published":"2003-03-01T00:00:00Z","publication_status":"published","intvolume":"        54","doi":"doi/10.1093/qjmath/54.1.11","publisher":"Oxford Academic","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","article_type":"original","oa_version":"None","abstract":[{"lang":"eng","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"}],"year":"2003","publication":"Quarterly Journal of Mathematics","issue":"1","author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","full_name":"Browning, Timothy D","last_name":"Browning"}],"scopus_import":"1","month":"03","title":"Counting rational points on diagonal quadratic surfaces","status":"public","date_updated":"2026-05-29T07:10:52Z"}]