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

Liyang Yang

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

Number Theory 2020-03-04 v2

Authors: Liyang Yang

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.

Keywords

adjoint L-functions cuspidal representations global field entireness general linear group

Cite

@article{arxiv.1903.09881,
  title  = {Holomorphy of Adjoint L-functions for $GL(n):$ $n\leq 4$},
  author = {Liyang Yang},
  journal= {arXiv preprint arXiv:1903.09881},
  year   = {2020}
}

Comments

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

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