Bounds for standard $L$-functions

TL;DR

This paper proves a subconvex bound for the standard L-function of cuspidal automorphic representations of GL(n) over Q, advancing understanding of L-function growth in the spectral and t-aspects.

Contribution

It establishes a subconvex bound for standard L-functions in the t-aspect and spectral aspect for automorphic representations of GL(n), extending previous bounds.

Findings

Proved subconvex bounds in the t-aspect.

Extended bounds to the spectral aspect with uniform parameter growth.

Improved understanding of L-function behavior for automorphic forms.

Abstract

Let $\pi$ be a cuspidal automorphic representation of a general linear group over the rational numbers. We establish a subconvex bound for the standard $L$-function of $\pi$ in the $t$-aspect. More generally, we address the spectral aspect in the case of uniform parameter growth.