{"type":"journal_article","publisher":"Elsevier","oa_version":"Published Version","date_updated":"2024-09-23T08:38:44Z","citation":{"mla":"Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number Curves.” <i>Advances in Mathematics</i>, vol. 457, 109946, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109946\">10.1016/j.aim.2024.109946</a>.","apa":"Chan, S. (2024). The average number of integral points on the congruent number curves. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2024.109946\">https://doi.org/10.1016/j.aim.2024.109946</a>","ama":"Chan S. The average number of integral points on the congruent number curves. <i>Advances in Mathematics</i>. 2024;457. doi:<a href=\"https://doi.org/10.1016/j.aim.2024.109946\">10.1016/j.aim.2024.109946</a>","short":"S. Chan, Advances in Mathematics 457 (2024).","chicago":"Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number Curves.” <i>Advances in Mathematics</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.aim.2024.109946\">https://doi.org/10.1016/j.aim.2024.109946</a>.","ieee":"S. Chan, “The average number of integral points on the congruent number curves,” <i>Advances in Mathematics</i>, vol. 457. Elsevier, 2024.","ista":"Chan S. 2024. The average number of integral points on the congruent number curves. Advances in Mathematics. 457, 109946."},"article_number":"109946","corr_author":"1","date_published":"2024-09-11T00:00:00Z","article_type":"original","language":[{"iso":"eng"}],"status":"public","day":"11","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.aim.2024.109946"}],"date_created":"2024-09-15T22:01:39Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Chan","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung","full_name":"Chan, Yik Tung","orcid":"0000-0001-8467-4106"}],"title":"The average number of integral points on the congruent number curves","volume":457,"_id":"18064","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2112.01615"]},"publication_status":"epub_ahead","abstract":[{"lang":"eng","text":" We show that the total number of non-torsion integral points on the elliptic curves ED : y\r\n2 = x3 − D2x, where D ranges over positive squarefree integers less than N, is O(N(log N)\r\n−1/4+ǫ). The proof involves a discriminant-lowering procedure on integral binary quartic forms and an application of Heath-Brown’s method on estimating the average size of the 2-Selmer group of the curves in this family."}],"intvolume":"       457","year":"2024","publication":"Advances in Mathematics","publication_identifier":{"issn":["0001-8708"],"eissn":["1090-2082"]},"doi":"10.1016/j.aim.2024.109946","quality_controlled":"1","scopus_import":"1","month":"09","department":[{"_id":"TiBr"}],"oa":1}