English

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

Number Theory 2021-05-11 v2 Representation Theory

Abstract

We show that the finite part of the adjoint LL function (including contributions from all nonarchimedean places, including ramified places) is holomorphic in (s)1/2\Re(s) \ge 1/2 for a cuspidal automorphic representation of GL3GL_3 over a number field. This improves the main result of [H16]. We obtain more general results for twisted adjoint LL functions of both GL3GL_3 and quasisplit unitary groups. For unitary groups, we explicate the relationship between poles of twisted adjoint LL functions, endoscopy, and the structure of the stable base change lifting.

Keywords

Cite

@article{arxiv.1808.06285,
  title  = {Adjoint L-functions for GL(3) and U(2,1)},
  author = {Joseph Hundley and Qing Zhang},
  journal= {arXiv preprint arXiv:1808.06285},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T03:37:55.724Z