Weak subconvexity for central values of $L$-functions

TL;DR

This paper introduces a general method to achieve weak subconvexity bounds for various $L$-functions, with applications to conjectures on the equidistribution of Hecke eigenforms.

Contribution

The paper presents a novel general approach to establish weak subconvexity bounds for multiple classes of $L$-functions, advancing understanding in analytic number theory.

Findings

Established a new method for weak subconvexity bounds

Applied the method to conjecture on mass equidistribution of Hecke eigenforms

Provided results relevant to Rudnick and Sarnak's conjecture

Abstract

We describe a general method to obtain weak subconvexity bounds for many classes of $L$-functions. This has applications to a conjecture of Rudnick and Sarnak for the mass equidistribution of Hecke eigenforms (see arxiv.org:math/0809.1636).