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Adjoint L-Functions for GL(3) and U2,1.

Authors :
Hundley, Joseph
Zhang, Qing
Source :
IMRN: International Mathematics Research Notices; Jan2021, Vol. 2021 Issue 1, p324-381, 58p
Publication Year :
2021

Abstract

We 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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10737928
Volume :
2021
Issue :
1
Database :
Complementary Index
Journal :
IMRN: International Mathematics Research Notices
Publication Type :
Academic Journal
Accession number :
148168683
Full Text :
https://doi.org/10.1093/imrn/rnz125