Holomorphy of Adjoint L-functions for $GL(n):$ $n\le 4$

Abstract

We show entireness of complete adjoint L-functions associated to \textbf{any} cuspidal representations of $\GL(3)$ or $\GL(4)$ over an arbitrary global field. Twisted cases are also investigated.

This is a revised version, with some typos and gaps fixed; some general results on Jacquet-Zagier trace formula on GL(n) has been separated out as an independent preprint and this paper is focused on adjoint L-functions; 40 pages