A Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Period |
Posted on:2013-10-05 | Degree:Ph.D | Type:Dissertation |
University:Temple University | Candidate:Daughton, Austin | Full Text:PDF |
GTID:1450390008990480 | Subject:Mathematics |
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. |
Keywords/Search Tags: | Automorphic, Correspondence, Log-polynomial, Dirichlet series, Finite, Period |
|
Related items |