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University of Illinois at Urbana-Champaign
Fourier Coefficients of Modular Forms and Their Applications
Abstract
dc:descriptionThe 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.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Masri, Nadia Rose
- Contributors dc:contributor
-
- Bruce, Berndt
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3337862
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86910