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Ahlgren, Scott Kilbourn, Timothy 2015-09-28T15:20:00Z 2015-09-28T15:20:00Z 10000-01-01 2007 2007 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. Made available in DSpace on 2015-09-28T15:20:00Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3290272.pdf: 1522560 bytes, checksum: 8be10954f01112e010d622f31affaaa5 (MD5) Previous issue date: 2007 Embargo set by: Seth Robbins for item 88167 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 66 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. http://hdl.handle.net/2142/86886 (MiAaPQ)AAI3290272 eng Mathematics Congruence Properties of Fourier Coefficients of Modular Forms text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.