The first moment of twisted Hecke $L$-functions with unbounded shifts

TL;DR

This paper calculates the average value of twisted Hecke L-functions at the first moment for prime power levels tending to infinity, considering various twists and shifts, advancing understanding of their distribution.

Contribution

It provides the first explicit computation of the first moment of twisted Hecke L-functions with unbounded shifts at prime power levels.

Findings

Explicit formula for the first moment of twisted Hecke L-functions.

Uniform results in conductor and vertical shift.

Insights into the distribution of these L-functions.

Abstract

We compute the first moment of twisted Hecke $L$-functions of prime power level going to infinity, uniformly in the conductor of the twist and in the vertical shift.