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

Abstract

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

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

References in corpus (1)

• Deducing Selberg trace formula via Rankin-Selberg method for ${\mathrm{GL}}_2$

Cited by in corpus (1)

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