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

Citation

Yang, Liyang (2021) A Coarse Jacquet-Zagier Trace Formula for GL(n) with Applications. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1j4r-pv26. https://resolver.caltech.edu/CaltechTHESIS:05272021-235254020

Abstract

In this thesis we establish a coarse Jacquet-Zagier trace identity fo GL(n). This formula connects adjoint L-functions on GL(n) with Artin L-functions attached to certain induced Galois representations. We prove the absolute convergence when Re(s) > 1, and obtain holomorphic continuation under almost all character twists. Moreover, as an application, we obtain that holomorphy of certain adjoint L-functions for GL(n) implies Dedekind conjecture of degree n. Some nonvanishing results are also proved.

Thesis Files