Bounds for moments of Dirichlet $L$-functions to a fixed modulus

Abstract

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

12 pages

References in corpus (2)

• Lower bounds for moments of zeta and $L$-functions revisited
• Sharp upper bounds for moments of quadratic Dirichlet $L$-functions