One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli

Peng Gao; Liangyi Zhao

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arXiv · 2005.04811

One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli

Peng Gao·Liangyi Zhao

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Abstract

In this paper, we study the one level density of low-lying zeros of a family of quadratic Hecke $L$-functions to prime moduli over the Gaussian field under the generalized Riemann hypothesis (GRH) and the ratios conjecture. As a corollary, we deduce that at least $75 \%$ of the members of this family do not vanish at the central point under GRH.

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Peng Gao, Liangyi Zhao. 2020-05-10. One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli. https://arxiv.org/abs/2005.04811

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