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Title:Fourier Coefficients of Modular Forms and Their Applications
Author(s):Masri, Nadia Rose
Doctoral Committee Chair(s):Bruce, Berndt
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
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.
Issue Date:2008
Type:Text
Language:English
Description:53 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008.
URI:http://hdl.handle.net/2142/86910
Other Identifier(s):(MiAaPQ)AAI3337862
Date Available in IDEALS:2015-09-28
Date Deposited:2008


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