Moments and One level density of certain unitary families of Hecke {$L$}-functions

TL;DR

This paper investigates the statistical properties of central values and low-lying zeros of specific families of Hecke L-functions over the Gaussian field, providing new insights into their non-vanishing and zero distribution.

Contribution

It introduces new results on moments, non-vanishing, and one level density for Hecke L-functions in the Gaussian field family, advancing understanding of their value distribution.

Findings

Quantitative non-vanishing results for central L-values

One level density results for low-lying zeros

Enhanced understanding of the distribution of zeros in these families

Abstract

In this paper, we study moments of central values of certain unitary families of Hecke $L$-functions of the Gaussian field, and establish quantitative non-vanishing result for the central values. We also establish an one level density result for the low-lying zeros of these families of Hecke $L$-functions.