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

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

2011-05-03

arxiv.org/abs/1105.0684v2

Mathematics

Number Theory

Corrected typos. To appear in the Ramanujan Journal

Scientific paper

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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