Two-divisibility of the coefficients of certain weakly holomorphic modular forms |
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Authors: | Darrin Doud Paul Jenkins John Lopez |
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Affiliation: | 1. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA
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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 τ-function, and use this to prove that these Fourier coefficients are often highly divisible by 2. |
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