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arXiv · 2503.17967

Murmurations of Hecke $L$-Functions of Imaginary Quadratic Fields

Zeyu Wang
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Abstract

We calculate the murmuration density for the family of Hecke $L$-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 $L$-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.

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Zeyu Wang. 2025-03-23. Murmurations of Hecke $L$-Functions of Imaginary Quadratic Fields. https://arxiv.org/abs/2503.17967

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