Hecke $L$ 函数的莫慕林现象
数论
2025-03-25 v1
摘要
We calculate the murmuration density for the family of Hecke -functions of imaginary quadratic fields associated to non-trivial characters. This density exhibits a universality property like Zubrilina's density for the murmurations of holomorphic modular forms. We show all murmuration functions obtained by averaging over the family with a compactly supported smooth weight function has asymptotics compatible with the 1-level density conjecture of Katz and Sarnak. The novelty of the murmurations of this family of -functions is its pronounced almost periodic feature, which allows one to describe this murmuration without averaging over primes, and which is non-existent or previously unnoticed for other families.
关键词
引用
@article{arxiv.2503.17967,
title = {Murmurations of Hecke $L$-Functions of Imaginary Quadratic Fields},
author = {Zeyu Wang},
journal= {arXiv preprint arXiv:2503.17967},
year = {2025}
}