Murmurations of Hecke $L$-Functions of Imaginary Quadratic Fields
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910889853059072 |
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| author | Wang, Zeyu |
| author_facet | Wang, Zeyu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17967 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Murmurations of Hecke $L$-Functions of Imaginary Quadratic Fields Wang, Zeyu Number Theory 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. |
| title | Murmurations of Hecke $L$-Functions of Imaginary Quadratic Fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.17967 |