超奇异等构图中环的分布

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-05-07 DOI:10.1016/j.jnt.2025.03.013

Eli Orvis

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引用次数: 0

摘要

Arpin et al.(2024)[2]最近的工作计算了超奇异的长度为r的环数。在本文中，我们将这项工作扩展到计算沿脊柱发生的循环次数。我们给出了这类循环的个数，以及当r和r固定时p→∞的平均值的公式。特别是，我们表明，当r不是2的幂时，长度为r的周期不成比例地可能沿着脊柱发生。我们提供了实验证据，证明这个结果在r是2的幂的情况下也成立。

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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Distribution of cycles in supersingular ℓ-isogeny graphs

Recent work by Arpin et al. (2024) [2] counted the number of cycles of length r in supersingular ℓ-isogeny graphs. In this paper, we extend this work to count the number of cycles that occur along the spine. We provide formulas for both the number of such cycles, and the average number as

p \to \infty

, with ℓ and r fixed. In particular, we show that when r is not a power of 2, cycles of length r are disproportionately likely to occur along the spine. We provide experimental evidence that this result holds in the case that r is a power of 2 as well.

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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.