A Lower Bound on the Proportion of Modular Elliptic Curves Over Galois CM Fields

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2023-11-02 DOI:10.1142/s1793042124500246

Zachary Feng

引用次数: 1

Abstract

We calculate an explicit lower bound on the proportion of elliptic curves that are modular over any Galois CM field not containing [Formula: see text]. Applied to imaginary quadratic fields, this proportion is at least [Formula: see text]. Applied to cyclotomic fields [Formula: see text] with [Formula: see text], this proportion is at least [Formula: see text] with only finitely many exceptions of [Formula: see text], for any choice of [Formula: see text].

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伽罗瓦CM域上模椭圆曲线比例的下界

我们计算了在任何伽罗瓦CM域上模化的椭圆曲线比例的显式下界，不包含[公式:见文本]。应用于虚二次域，这个比例至少为[公式:见文本]。将[公式:见文]与[公式:见文]应用于切眼圈领域，这个比例至少为[公式:见文]，只有[公式:见文]有有限的例外，任何[公式:见文]的选择。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.