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Congruences for coefficients of level 2 modular functions with poles at 0

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Abstract

We give congruences modulo powers of 2 for the Fourier coefficients of certain level 2 modular functions with poles only at 0, answering a question posed by Andersen and the first author. The congruences involve a modulus that depends on the binary expansion of the modular form’s order of vanishing at \(\infty \).

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Correspondence to Paul Jenkins.

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This work was partially supported by a grant from the Simons Foundation (\(\# 281876\) to Paul Jenkins).

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Jenkins, P., Keck, R. & Moss, E. Congruences for coefficients of level 2 modular functions with poles at 0. Arch. Math. 111, 369–378 (2018). https://doi.org/10.1007/s00013-018-1207-8

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