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oai:www.ideals.illinois.edu:2142/86910 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Bruce, Berndt Masri, Nadia Rose 2015-09-28T15:20:08Z 2015-09-28T15:20:08Z 10000-01-01 2008 2008 The theory of modular forms, as it has been developed over the past several decades, has highlighted deep connections between the areas of analytic and algebraic number theory and arithmetic geometry. In this thesis we explore some applications. First, we give some new and simpler proofs of recent results of S.C. Milne, that derive formulas for some infinite families of identities for sums of integer squares. Next, we extend some results of Ahlgren, Ono and Papanikolas, defining an analogue of the classical higher Weierstrass points on X0(p) and obtaining a precise relationship of these with supersingular j-invariants. Made available in DSpace on 2015-09-28T15:20:08Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3337862.pdf: 651299 bytes, checksum: 73ee8ed7887ef3dfab054d19b48c3a7c (MD5) Previous issue date: 2008 Embargo set by: Seth Robbins for item 88191 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 53 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. http://hdl.handle.net/2142/86910 (MiAaPQ)AAI3337862 eng Mathematics Fourier Coefficients of Modular Forms and Their Applications text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.