Congruence Properties of Fourier Coefficients of Modular Forms

66 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 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.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD