×

One level density of low-lying zeros of quadratic Hecke \(L\)-functions to prime moduli. (English) Zbl 1480.11105

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.

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
PDFBibTeX XMLCite
Full Text: arXiv Link