English

A Coarse Jacquet-Zagier Trace Formula for GL($n$) with Applications

Number Theory 2026-05-13 v2

Abstract

In this paper we establish a coarse Jacquet-Zagier trace identity for GL(n).(n). We prove the absolute convergence when (s)>1\Re(s)>1 and 0<(s)<1;0<\Re(s)<1; and obtain holomorphic continuation under almost all character twist. Moreover, as an application, we prove that holomorphy of certain adjoint LL-functions for GL(n)(n) implies Dedekind conjecture of degree nn. Some nonvanishing results are also discussed.

Keywords

Cite

@article{arxiv.2003.03450,
  title  = {A Coarse Jacquet-Zagier Trace Formula for GL($n$) with Applications},
  author = {Liyang Yang},
  journal= {arXiv preprint arXiv:2003.03450},
  year   = {2026}
}

Comments

139 pages; the previous arXiv:1903.09881 has been split into two parts, this is the second half

R2 v1 2026-06-23T14:07:06.741Z