Congruences for the Coefficients of Weakly Holomorphic Modular Forms

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https://hdl.handle.net/2142/86871

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
Permalink: http://hdl.handle.net/2142/86871

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