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University of Illinois at Urbana-Champaign
Congruence Properties of Fourier Coefficients of Modular Forms
Abstract
dc:descriptionFourier 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.
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
-
- Kilbourn, Timothy
- Contributors dc:contributor
-
- Ahlgren, Scott
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3290272
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86886