Shifted moments of modular $L$-functions to a fixed level

TL;DR

This paper derives upper bounds for shifted moments of modular L-functions at a fixed prime level, assuming the generalized Riemann hypothesis, advancing understanding of their size and distribution.

Contribution

It provides the first upper bounds for shifted moments of modular L-functions at a fixed prime level under GRH, a significant step in analytic number theory.

Findings

Established upper bounds for shifted moments under GRH

Results applicable to fixed prime level L-functions

Contributes to understanding of L-function value distribution

Abstract

We establish upper bounds for shifted moments of modular $L$-functions to a fixed prime level under the generalized Riemann hypothesis.