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Title:Congruence Properties of Fourier Coefficients of Modular Forms
Author(s):Kilbourn, Timothy
Doctoral Committee Chair(s):Ahlgren, Scott
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:Fourier coefficients of modular forms have profound connections with many areas of number theory. We will consider three different applications of these coefficients. First, we extend the Apery number supercongruence, proving an observation of Rodriguez-Villegas. Second, we prove an analogue of Newman's Conjecture with prime-power moduli for a class of partition functions. Finally, we prove some results about the integrality of Fourier coefficients of cusp forms at cusps other than infinity.
Issue Date:2007
Type:Text
Language:English
Description:66 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.
URI:http://hdl.handle.net/2142/86886
Other Identifier(s):(MiAaPQ)AAI3290272
Date Available in IDEALS:2015-09-28
Date Deposited:2007


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