Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods

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.

Grantor dc:publisher

Temple University. Libraries

Year dc:date.issued

2012

Author dc:creator

• Daughton, Austin James Chinault

Advisor dc:contributor.advisor

• Knopp, Marvin Isadore, 1933-

Committee members dc:contributor.committeemember

• Datskovsky, Boris Abramovich
• Berhanu, Shiferaw
• Mendoza, Gerardo A.
• Pribitkin, Wladimir

• Mathematics
• Automorphic Forms
• Automorphic Integrals
• Hecke Correspondence
• Number Theory

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Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

eng

Dc Identifier Other

864885462

OAI identifier oai:identifier

oai:scholarshare.temple.edu:20.500.12613/1054