[{"arxiv":1,"publisher":"Université de Bordeaux","year":"2025","type":"journal_article","citation":{"short":"Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988.","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>","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.","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>.","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>","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>."},"external_id":{"arxiv":["2408.03774"]},"date_updated":"2026-07-16T08:45:12Z","tmp":{"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)","image":"/image/cc_by_nd.png","short":"CC BY-ND (4.0)"},"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.","scopus_import":"1","month":"11","quality_controlled":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file":[{"file_size":766196,"checksum":"67aa0afbc0b5bcbff5341f4d25e6ba20","relation":"main_file","date_created":"2025-12-29T10:05:22Z","file_id":"20861","access_level":"open_access","file_name":"2025_JTNB_Diao.pdf","success":1,"content_type":"application/pdf","creator":"dernst","date_updated":"2025-12-29T10:05:22Z"}],"date_published":"2025-11-27T00:00:00Z","intvolume":"        37","volume":37,"file_date_updated":"2025-12-29T10:05:22Z","author":[{"id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b","first_name":"Yijie","orcid":"0000-0002-4989-5330","full_name":"Diao, Yijie","last_name":"Diao"}],"supplementarymaterial":"no","publication_identifier":{"issn":["1246-7405"],"eissn":["2118-8572"]},"has_accepted_license":"1","publication":"Journal de theorie des nombres de Bordeaux","researchdata_availability":"no","oa":1,"abstract":[{"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":"eng"},{"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.","lang":"fre"}],"OA_type":"hybrid","das_tickbox":"0","oa_version":"Published Version","day":"27","OA_place":"publisher","language":[{"iso":"eng"}],"ddc":["510"],"_id":"20850","license":"https://creativecommons.org/licenses/by-nd/4.0/","doi":"10.5802/jtnb.1348","publication_status":"published","page":"973-988","article_processing_charge":"Yes (in subscription journal)","article_type":"original","department":[{"_id":"TiBr"}],"date_created":"2025-12-21T23:01:35Z","title":"Class numbers and integer points on some Pellian surfaces","status":"public","issue":"3","corr_author":"1"},{"abstract":[{"lang":"eng","text":"Let X be a sufficiently large positive integer. We prove that one may choose a subset S of primes with cardinality O(logX) such that a positive proportion of integers less than X can be represented by x2+py2 for at least one p∈S."}],"oa":1,"language":[{"iso":"eng"}],"day":"09","oa_version":"Preprint","_id":"12406","doi":"10.4064/aa210830-24-11","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2103.08268","open_access":"1"}],"publication_status":"published","isi":1,"page":"1-17","article_processing_charge":"No","article_type":"original","status":"public","date_created":"2023-01-26T21:17:04Z","title":"Density of the union of positive diagonal binary quadratic forms","department":[{"_id":"GradSch"}],"corr_author":"1","publisher":"Instytut Matematyczny","arxiv":1,"type":"journal_article","year":"2023","external_id":{"isi":["000912903000001"],"arxiv":["2103.08268"]},"citation":{"short":"Y. Diao, Acta Arithmetica 207 (2023) 1–17.","apa":"Diao, Y. (2023). Density of the union of positive diagonal binary quadratic forms. <i>Acta Arithmetica</i>. Instytut Matematyczny. <a href=\"https://doi.org/10.4064/aa210830-24-11\">https://doi.org/10.4064/aa210830-24-11</a>","chicago":"Diao, Yijie. “Density of the Union of Positive Diagonal Binary Quadratic Forms.” <i>Acta Arithmetica</i>. Instytut Matematyczny, 2023. <a href=\"https://doi.org/10.4064/aa210830-24-11\">https://doi.org/10.4064/aa210830-24-11</a>.","ista":"Diao Y. 2023. Density of the union of positive diagonal binary quadratic forms. Acta Arithmetica. 207, 1–17.","ieee":"Y. Diao, “Density of the union of positive diagonal binary quadratic forms,” <i>Acta Arithmetica</i>, vol. 207. Instytut Matematyczny, pp. 1–17, 2023.","mla":"Diao, Yijie. “Density of the Union of Positive Diagonal Binary Quadratic Forms.” <i>Acta Arithmetica</i>, vol. 207, Instytut Matematyczny, 2023, pp. 1–17, doi:<a href=\"https://doi.org/10.4064/aa210830-24-11\">10.4064/aa210830-24-11</a>.","ama":"Diao Y. Density of the union of positive diagonal binary quadratic forms. <i>Acta Arithmetica</i>. 2023;207:1-17. doi:<a href=\"https://doi.org/10.4064/aa210830-24-11\">10.4064/aa210830-24-11</a>"},"date_updated":"2024-10-21T06:01:30Z","scopus_import":"1","acknowledgement":"This article is a version the author’s master thesis at the University of Bonn. The author would like to thank his advisor Valentin Blomer for introducing the problem, and giving generous feedback and encouragement along the way, especially during the global pandemic.\r\nThe author thanks Edgar Assing for his lectures on analytic number theory. Finally, the author is grateful to the anonymous referees for their valuable time and comments.\r\n","keyword":["Algebra","Number Theory"],"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"01","date_published":"2023-01-09T00:00:00Z","volume":207,"intvolume":"       207","author":[{"first_name":"Yijie","id":"7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b","orcid":"0000-0002-4989-5330","last_name":"Diao","full_name":"Diao, Yijie"}],"publication_identifier":{"eissn":["1730-6264"],"issn":["0065-1036"]},"publication":"Acta Arithmetica"}]