Congruence Properties of Fourier Coefficients of Modular Forms
Kilbourn, Timothy
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https://hdl.handle.net/2142/86886
Description
Title
Congruence Properties of Fourier Coefficients of Modular Forms
Author(s)
Kilbourn, Timothy
Issue Date
2007
Doctoral Committee Chair(s)
Ahlgren, Scott
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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