Peng Gao ; Liangyi Zhao - One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli

hrj:7461 - Hardy-Ramanujan Journal, May 6, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020 - https://doi.org/10.46298/hrj.2021.7461
One level density of low-lying zeros of quadratic Hecke L-functions to prime moduli

Authors: Peng Gao ; Liangyi Zhao

    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.

    https://doi.org/10.46298/hrj.2021.7461
    Source : oai:HAL:hal-03208534v1
    Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020
    Published on: May 6, 2021
    Accepted on: May 6, 2021
    Submitted on: May 5, 2021
    Keywords: quadratic Hecke L-function,one level density,low-lying zeros,2010 Mathematics Subject Classification. 11M06, 11M26, 11M50,[MATH]Mathematics [math]

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