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

Peng Gao (1) , Liangyi Zhao

1 BUAA - Beihang University

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.

Mots clés: low-lying zeros; one level density; quadratic Hecke L-function

Domaines: Mathématiques [math]

Peng Gao, Liangyi Zhao. One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli. Hardy-Ramanujan Journal, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020, pp.173-187. ⟨10.46298/hrj.2021.7461⟩. ⟨hal-03208534⟩