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Dissertation/Thesis Abstract

A Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods
by Daughton, Austin, Ph.D., Temple University, 2012, 53; 3509049
Abstract (Summary)

Since Hecke first proved his correspondence between Dirichlet series with functional equations and automorphic forms, there have been a great number of generalizations. Of particular interest is a generalization due to Bochner that gives a correspondence between Dirichlet series with any finite number of poles that satisfy the classical functional equation and automorphic integrals with (finite) log-polynomial sum period functions.

In this dissertation, we extend Bochner's result to Dirichlet series with finitely many essential singularities. With some restrictions on the underlying group and the weight, we also prove a correspondence for Dirichlet series with infinitely many poles. For this second correspondence, we provide a technique to approximate automorphic integrals with infinite log-polynomial sum period functions by automorphic integrals with finite log-polynomial period functions.

Indexing (document details)
Advisor: Knopp, Marvin I.
Commitee: Berhanu, Shiferaw, Datskovsky, Boris A., Mendoza, Gerardo, Pribitkin, Wladimir
School: Temple University
Department: Mathematics
School Location: United States -- Pennsylvania
Source: DAI-B 73/09(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Automorphic forms, Automorphic integrals, Hecke correspondence, Number theory
Publication Number: 3509049
ISBN: 978-1-267-35198-2
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