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arXiv · 1105.0684

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

Darrin Doud·Paul Jenkins·John Lopez
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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.

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Darrin Doud, Paul Jenkins, John Lopez. 2011-07-29. Two-divisibility of the coefficients of certain weakly holomorphic modular forms. https://doi.org/10.1007/s11139-011-9331-0

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