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Two-divisibility of the coefficients of certain weakly holomorphic modular forms

By Darrin Doud, Paul Jenkins and John Lopez

Abstract

We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly divisible by 2.Comment: Corrected typos. To appear in the Ramanujan Journa

Topics: Mathematics - Number Theory, 11F33, 11F11
Year: 2011
DOI identifier: 10.1007/s11139-011-9331-0
OAI identifier: oai:arXiv.org:1105.0684
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