New error term for the fourth moment of automorphic L functions

TL;DR

This paper refines the error term in the asymptotic formula for the twisted fourth moment of automorphic L functions, leading to improved bounds in subconvexity and non-vanishing proportions.

Contribution

It introduces a new error term for the fourth moment of automorphic L functions, enhancing previous results and deriving stronger bounds.

Findings

Improved error term in the asymptotic formula

New subconvexity bound in the level aspect

Enhanced lower bound on non-vanishing proportion

Abstract

We improve the error term in the asymptotic formula for the twisted fourth moment of automorphic L functions of prime level and weight two proved by Kowalski, Michel and Vanderkam. As a consequence, we obtain a new subconvexity bound in the level aspect and improve the lower bound on proportion of simultaneous non-vanishing.