University of Illinois at Urbana-Champaign
Congruences for the Coefficients of Weakly Holomorphic Modular Forms
Abstract
dc:descriptionRecent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. In each case, the values of the given arithmetic function appear as the Fourier coefficients of a weakly holomorphic modular form. We show that similar congruences exist for the coefficients of any weakly holomorphic modular form on any congruence subgroup Gamma0(N). In particular, we give congruences for a wide class of partition functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level. Finally, we make a more general statement about simultaneous congruences for the coefficients of weakly holomorphic modular forms on Gamma1(N).
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
-
- Treneer, Stephanie
- Contributors dc:contributor
-
- Ahlgren, Scott
Subjects
dc:subject × 1Rights
- Language dc:language
- eng
Identifiers
dc:identifier.*- Identifier
- (MiAaPQ)AAI3243013
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/86871