A uniform asymptotic formula for the second moment of primitive L-functions on the critical line

TL;DR

This paper derives a uniform asymptotic formula for the second moment of automorphic L-functions of even weight and prime power level, with error estimates valid across all parameters such as level, weight, shift, and twist.

Contribution

It provides a new uniform asymptotic formula for the second moment of automorphic L-functions, improving error estimates across multiple parameters.

Findings

Asymptotic formula established for second moment

Error term estimated uniformly in all parameters

Results applicable to automorphic L-functions of prime power level

Abstract

We prove an asymptotic formula for the second moment of automorphic L-functions of even weight and prime power level. The error term is estimated uniformly in all parameters: level, weight, shift and twist.