Bounds for moments of quadratic Dirichlet character sums of prime moduli

TL;DR

This paper establishes sharp upper bounds for moments of quadratic Dirichlet L-functions and character sums with prime moduli, assuming GRH, advancing understanding of their behavior in number theory.

Contribution

It provides the first sharp bounds for moments of quadratic Dirichlet L-functions and character sums with prime moduli under GRH assumptions.

Findings

Sharp upper bounds for shifted moments of quadratic Dirichlet L-functions

Bounds for moments of quadratic Dirichlet character sums with prime moduli

Results depend on the generalized Riemann hypothesis

Abstract

Assuming the generalized Riemann hypothesis, we evaluate sharp upper bounds for the shifted moments of quadratic Dirichlet L-functions with moduli 8p, where p ranges over odd primes. We then apply this result to prove bounds for the moments of quadratic Dirichlet character sums with prime moduli.