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

TL;DR

This paper investigates the non-vanishing of central values of quadratic Hecke L-functions over Gaussian primes, showing that over 9% of these functions do not vanish at the center, using mollified moments.

Contribution

It provides the first non-vanishing result for quadratic Hecke L-functions of prime moduli in the Gaussian field, employing mollified moment techniques.

Findings

More than 9% of the family do not vanish at the central point.

First non-vanishing result for this family in the Gaussian field.

Uses mollified moments to establish non-vanishing proportion.

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.