Adjoint L-functions for GL(3) and U(2,1)

Abstract

We show that the finite part of the adjoint $L$ function (including contributions from all nonarchimedean places, including ramified places) is holomorphic in $\Re (s)\ge 1/2$ for a cuspidal automorphic representation of $G{L}_3$ over a number field. This improves the main result of [H16]. We obtain more general results for twisted adjoint $L$ functions of both $G{L}_3$ 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.

Introduction is rewritten. The order of section 2 and section 3 are switched

References in corpus (2)

• Plancherel distribution of Satake parameters of Maass cusp forms on $G{L}_3$
• On the Archimedean Local Gamma Factors for Adjoint Representation of ${\mathrm{GL}}_3$, Part I

Cited by in corpus (1)

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