Murmurations of elliptic curves
Number Theory
2024-08-06 v2 High Energy Physics - Theory
Machine Learning
Abstract
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.
Cite
@article{arxiv.2204.10140,
title = {Murmurations of elliptic curves},
author = {Yang-Hui He and Kyu-Hwan Lee and Thomas Oliver and Alexey Pozdnyakov},
journal= {arXiv preprint arXiv:2204.10140},
year = {2024}
}
Comments
27 pages, 16 figures, 2 tables