椭圆曲线 3-isogeny induced Selmer 群的统计量

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-10-31 DOI:10.1016/j.jnt.2024.09.003

Pratiksha Shingavekar

引用次数: 0

摘要

给定一个六次幂自由整数 a，设 Ea 是由 y2=x3+a 定义的椭圆曲线。我们证明了六次幂自由整数 a 的低密度的明确结果，对于这些低密度的六次幂自由整数 a，Ea 在 Q(μ3) 上的 3-isogeny induced Selmer 群的维数≤1。这些结果是通过改进达文波特-海尔布隆的策略，将积分二元三次形式的统计量与 3-isogeny induced Selmer 群的统计量联系起来而证明的。

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Statistics for 3-isogeny induced Selmer groups of elliptic curves

Given a sixth power free integer a, let

E_{a}

be the elliptic curve defined by

y^{2} = x^{3} + a

. We prove explicit results for the lower density of sixth power free integers a for which the 3-isogeny induced Selmer group of

E_{a}

over

Q (μ_{3})

has dimension ≤1. The results are proven by refining the strategy of Davenport–Heilbronn, by relating the statistics for integral binary cubic forms to the statistics for 3-isogeny induced Selmer groups.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.