Document Type

Dissertation

Date of Degree

Summer 2011

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Yangbo Ye

First Committee Member

Yangbo Ye

Second Committee Member

Philip Kutzko

Third Committee Member

Palle Jorgensen

Fourth Committee Member

Muthu Krishnamurthy

Fifth Committee Member

Richard Dykstra

Abstract

In this paper we deduce a prime number theorem for the L-function L(s; AIE=Q() AIF=Q(0)) where and 0 are automorphic cuspidal representations of GLn=E and GLm=F, respectively, with E and F solvable algebraic number elds with a Galois invariance assumption on the representations. Here AIF=Q denotes the automorphic induction functor. We then use the proof of the prime number theorem to compute the n-level correlation function of a product of L-functions dened over cyclic algebraic number elds of prime degree.

Keywords

base change, L-function

Pages

iii, 68 pages

Bibliography

Includes bibliographical references (pages 66-68).

Copyright

Copyright 2011 Timothy Lee Gillespie

Included in

Mathematics Commons

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