Gao, Peng; Zhao, Liangyi One level density of low-lying zeros of quadratic Hecke \(L\)-functions to prime moduli. (English) Zbl 1480.11105 Hardy-Ramanujan J. 43, 173-187 (2020). Summary: 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. Cited in 2 Documents MSC: 11M06 \(\zeta (s)\) and \(L(s, \chi)\) 11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses 11M50 Relations with random matrices Keywords:low-lying zeros; one level density; quadratic Hecke \(L\)-function PDFBibTeX XMLCite \textit{P. Gao} and \textit{L. Zhao}, Hardy-Ramanujan J. 43, 173--187 (2020; Zbl 1480.11105) Full Text: arXiv Link