Murmurations of modular forms in the weight aspect
Number Theory
2026-02-18 v2
Abstract
We prove the existence of "murmurations" in the family of holomorphic modular forms of level and weight , that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor. This is the first demonstration of murmurations in an archimedean family.
Keywords
Cite
@article{arxiv.2310.07746,
title = {Murmurations of modular forms in the weight aspect},
author = {Jonathan Bober and Andrew R. Booker and Min Lee and David Lowry-Duda},
journal= {arXiv preprint arXiv:2310.07746},
year = {2026}
}
Comments
30 pages, to appear in Algebra & Number Theory