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


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.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Trace formula, automorphic forms, L-functions, holomorphic continuation
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Scott Russell Johnson Graduate Dissertation Prize in Mathematics, 2021. Apostol Award for Excellence in Teaching in Mathematics, 2021. Scott Russell Johnson Prize for Excellence in Graduate Studies, 2018, 2019. Scott Russell Johnson Prize for Excellence as a First-Year Graduate Student, 2017.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ramakrishnan, Dinakar
Thesis Committee:
  • Zhu, Xinwen (chair)
  • Ramakrishnan, Dinakar
  • Mantovan, Elena
  • Burungale, Ashay
Defense Date:17 May 2021
Non-Caltech Author Email:yangliyang12 (AT)
Record Number:CaltechTHESIS:05272021-235254020
Persistent URL:
Yang, Liyang0000-0001-6988-2927
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14185
Deposited By: Liyang Yang
Deposited On:03 Jun 2021 00:25
Last Modified:03 Nov 2021 19:45

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