Moments and Non-vanishing of central values of Quadratic Hecke $L$-functions in the Gaussian Field

Abstract

We evaluate the first three moments of central values of a family of qudratic Hecke $L$-functions in the Gaussian field with power saving error terms. In particular, we obtain asymptotic formulas for the first two moments with error terms of size $O(X^{1/2+\epsilon })$. We also study the first and second mollified moments of the same family of $L$-functions to show that at least $87.5\%$ of the members of this family have non-vanishing central values.

25 pages

References in corpus (3)

• One level density of low-lying zeros of quadratic and quartic Hecke $L$-functions
• Moments of Quadratic Hecke $L$-functions of Imaginary Quadratic Number Fields
• The fourth moment of quadratic Dirichlet $L$-functions

Cited by in corpus (4)

• The fourth moment of central values of quadratic Hecke $L$-functions in the Gaussian field
• Non-vanishing of central values of quadratic Hecke $L$-functions of prime moduli in the Gaussian field
• Real zeros of quadratic Hecke $L$-functions
• One level density of low-lying zeros of quadratic Hecke $L$-functions to prime moduli