AdjointL-Functions for GL(3) and U2,1

Abstract

AbstractWe show that the finite part of the adjoint $L$-function (including contributions from all non-archimedean places, including ramified places) is holomorphic in ${\textrm{Re}}(s) \ge 1/2$ for a cuspidal automorphic representation of ${\textrm{GL}}_3$ over a number field. This improves the main result of [21]. We obtain more general results for twisted adjoint $L$-functions of both ${\textrm{GL}}_3$ and quasisplit unitary groups. For unitary groups, we explicate the relationship between poles of twisted adjoint $L$-functions, endoscopy, and the structure of the stable base change lifting.