Bounds for moments of modular $L$-functions to a fixed modulus
Volume 205 / 2022
Acta Arithmetica 205 (2022), 161-189
MSC: Primary 11M06.
DOI: 10.4064/aa211124-24-6
Published online: 22 September 2022
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 $k \geq 0$ and sharp upper bounds for $0 \leq k \leq 1$.
