Weak subconvexity without a Ramanujan hypothesis

TL;DR

This paper introduces a novel approach to establish weak subconvexity bounds for automorphic L-functions using mild hypotheses and a new zero density estimate, advancing understanding in analytic number theory.

Contribution

It presents a new method for weak subconvexity bounds applicable to all automorphic L-functions, relying on a zero density estimate without assuming the Ramanujan hypothesis.

Findings

Verified hypotheses for all automorphic L-functions

Established unconditional log-free zero density estimate

Achieved weak subconvexity bounds without Ramanujan hypothesis

Abstract

We describe a new method to obtain weak subconvexity bounds for $L$-functions with mild hypotheses on the size of the Dirichlet coefficients. We verify these hypotheses for all automorphic $L$-functions and (with mild restrictions) the Rankin-Selberg $L$-functions attached to two automorphic representations. The proof relies on a new unconditional log-free zero density estimate for Rankin-Selberg $L$-functions.