Bounds for standard $L$-functions

Abstract

Let $\ddot{I}€$ 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 $\ddot{I}€$ in the $t$-aspect. More generally, we address the spectral aspect in the case of uniform parameter growth.

256 pages. v3: improved exposition, minor corrections/clarifications