Murmurations of Elliptic Curves

被引：2

作者：

He, Yang-Hui ^{[1
,2
]}

Lee, Kyu-Hwan ^{[3
,4
]}

Oliver, Thomas ^{[5
]}

Pozdnyakov, Alexey ^{[3
]}

机构：

[1] Royal Inst Great Britain, London Inst Math Sci, London, England

[2] City Univ London, Dept Math, London, England

[3] Univ Connecticut, Dept Math, Storrs, CT USA

[4] Korea Inst Adv Study, Seoul, South Korea

[5] Univ Westminster, London, England

来源：

EXPERIMENTAL MATHEMATICS | 2024年

基金：

英国工程与自然科学研究理事会;

关键词：

Elliptic curves; L-functions; principal component analysis; logistic regression; machine learning;

D O I：

10.1080/10586458.2024.2382361

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking oscillating pattern, the details of which vary with the rank. Based on this observation, we perform various data-scientific experiments with the goal of classifying elliptic curves according to their ranks.

引用

页数：13

共 20 条

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