椭圆曲线fp点群的循环性和可整除性的平均同余类偏置

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-06-18 DOI:10.1016/j.jnt.2025.05.003

Sung Min Lee

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引用次数: 0

摘要

2009年，W.D. Banks和I.E. Shparlinski研究了p≤x的素数的平均密度，对于这些素数，小高度模p的椭圆曲线的约简满足一定的代数性质，即点数可被固定整数m的循环性和可整除性。本文通过将所考虑的素数p限定在等差数列kmodn中，改进了他们的结果。此外，对于固定模n，我们研究了满足上述性质的素数的不同同余类kmodn之间的统计偏差。

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On the average congruence class bias for cyclicity and divisibility of the groups of Fp-points of elliptic curves

In 2009, W.D. Banks and I.E. Shparlinski studied the average densities of primes

p \leq x

for which the reductions of elliptic curves of small height modulo p satisfy certain algebraic properties, namely cyclicity and divisibility of the number of points by a fixed integer m. In this paper, we refine their results by restricting the primes p under consideration to lie in an arithmetic progression

k \mod n

. Furthermore, for a fixed modulus n, we investigate statistical biases among the different congruence classes

k \mod n

of primes satisfying the aforementioned properties.

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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.