Machine learning the vanishing order of rational L-functions
Number Theory
2025-02-19 v1 High Energy Physics - Theory
Abstract
In this paper, we study the vanishing order of rational -functions from a data scientific perspective. Each -function is represented in our data by finitely many Dirichlet coefficients, the normalisation of which depends on the context. We observe murmuration-like patterns in averages across our dataset, find that PCA clusters rational -functions by their vanishing order, and record that LDA and neural networks may accurately predict this quantity.
Cite
@article{arxiv.2502.10360,
title = {Machine learning the vanishing order of rational L-functions},
author = {Joanna Bieri and Giorgi Butbaia and Edgar Costa and Alyson Deines and Kyu-Hwan Lee and David Lowry-Duda and Thomas Oliver and Yidi Qi and Tamara Veenstra},
journal= {arXiv preprint arXiv:2502.10360},
year = {2025}
}
Comments
16 pages, 18 figures, 8 tables