Non-vanishing of central values of quadratic Hecke $L$-functions of prime moduli in the Gaussian field

Abstract

We study the first and second mollified moments of central values of a quadratic family of Hecke $L$-functions of prime moduli to show that more than nine percent of the members of this family do not vanish at the central values.

37 pages

References in corpus (3)

• One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions
• Moments and Non-vanishing of central values of Quadratic Hecke $L$-functions in the Gaussian Field
• The fourth moment of central values of quadratic Hecke $L$-functions in the Gaussian field