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

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.

11 pages

References in corpus (5)

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