ANALYTIC RANKS OF ELLIPTIC CURVES OVER NUMBER FIELDS

被引：0
作者：
Cho, Peter J. [1 ]
机构：
[1] Ulsan Natl Inst Sci & Technol, Dept Math Sci, Ulsan, South Korea
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年
基金：
新加坡国家研究基金会;
关键词：
Elliptic curve; analytic rank; cyclic extension;
D O I：
10.1090/proc/16182
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let E be an elliptic curve over Q. Then, we show that the average analytic rank of E over cyclic extensions of degree l over Q with l a prime not equal to 2, is at most 2+rQ(E), where rQ(E) is the analytic rank of the elliptic curve E over Q. This bound is independent of the degree l. Using a recent result of Bhargava, Taniguchi and Thorne [Improved error estimates for the Davenport-Heilbronn theorems, arxiv.org/abs/2107.12819, 2021], we obtain a non-trivial upper bound on the average analytic rank of E over S3-fields.
引用
收藏
页码：1403 / 1414
页数：12
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