Moments of central values of quartic Dirichlet $L$-functions

TL;DR

This paper investigates the average behavior of the central values of quartic Dirichlet L-functions and proves that a positive proportion of these values do not vanish.

Contribution

It provides the first quantitative non-vanishing results for the central values of quartic Dirichlet L-functions.

Findings

Established non-vanishing proportion of quartic Dirichlet L-functions at the central point.

Derived asymptotic formulas for moments of these L-values.

Enhanced understanding of the distribution of quartic Dirichlet L-values.

Abstract

In this paper, we study moments of the central values of quartic Dirichlet $L$-functions and establish quantitative non-vanishing result for these $L$-values.