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

Abstract

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

13 pages. arXiv admin note: text overlap with arXiv:2103.00149