Fourier Coefficients of Modular Forms and Their Applications
Masri, Nadia Rose
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https://hdl.handle.net/2142/86910
Description
Title
Fourier Coefficients of Modular Forms and Their Applications
Author(s)
Masri, Nadia Rose
Issue Date
2008
Doctoral Committee Chair(s)
Bruce, Berndt
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
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.
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