Bounds for Moments of Dirichlet $L$-functions of fixed modulus on the critical line

Abstract

We study the $2k$-th moment of the family of Dirichlet $L$-functions to a fixed prime modulus on the critical line and establish sharp lower bounds for all real $k\ge 0$ and sharp upper bounds for $k$ in the range $0\le k\le 1$.

7 pages