Congruences for the Coefficients of Weakly Holomorphic Modular Forms

Treneer, Stephanie

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Description

Title

Congruences for the Coefficients of Weakly Holomorphic Modular Forms

Author(s)

Treneer, Stephanie

Issue Date

2006

Doctoral Committee Chair(s)

Ahlgren, Scott

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

Recent 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).

Graduation Semester

2006

Type of Resource

text

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