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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.
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https://hal.archives-ouvertes.fr/hal-03208534
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Submitted on : Monday, April 26, 2021 - 4:03:42 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Tuesday, July 27, 2021 - 7:27:50 PM

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

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