The average number of integral points on the congruent number curves

被引：0
作者：
Chan, Stephanie [1 ,2 ]
机构：
[1] Univ Michigan, Dept Math, 530 Church St, Ann Arbor, MI 48109 USA
[2] IST Austria, Campus 1, A-3400 Klosterneuburg, Austria
来源：
ADVANCES IN MATHEMATICS | 2024年 / 457卷
关键词：
Elliptic curve; Quadratic twist; Integral point; SELMER GROUPS; THEOREM; SIZE;
D O I：
10.1016/j.aim.2024.109946
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the total number of non-torsion integral points on the elliptic curves epsilon(D): y(2) = x(3) -D(2)x, where D ranges over positive squarefree integers less than N , is O ( N (log N ) (- 1/4 +E )). The proof involves a discriminant-lowering procedure on integral binary quartic forms and an application of HeathBrown's method on estimating the average size of the 2-Selmer groups of the curves in this family. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
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页数：31
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