Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli

TL;DR

This paper derives sharp bounds for the moments of quadratic Dirichlet L-functions at the central point for prime-related moduli, assuming GRH, advancing understanding of their value distribution.

Contribution

It provides the first sharp upper and lower bounds for moments of quadratic Dirichlet L-functions of prime-related moduli under GRH.

Findings

Established bounds for the $k$-th moments for all real $k \\geq 0$

Results are sharp and valid under the generalized Riemann hypothesis

Focus on moduli of the form $8p$ with $p$ prime

Abstract

In this paper, we study the $k$-th moment of central values of the family of quadratic Dirichlet $L$-functions of moduli $8p$, with $p$ ranging over odd primes. Assuming the truth of the generlized Riemann hypothesis, we establish sharp upper and lower bounds for the $k$-th power moment of these $L$-values for all real $k \geq 0$.