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arXiv · 2001.04337

Congruences for coefficients of modular functions in levels 3, 5, and 7 with poles at 0

Paul Jenkins·Ryan Keck
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Abstract

We give congruences modulo powers of $p \in \{3, 5,7\}$ for the Fourier coefficients of certain modular functions in level $p$ with poles only at 0, answering a question posed by Andersen and the first author and continuing work done by the authors and Moss. The congruences involve a modulus that depends on the base $p$ expansion of the modular form's order of vanishing at $\infty$.

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Paul Jenkins, Ryan Keck. 2020-01-10. Congruences for coefficients of modular functions in levels 3, 5, and 7 with poles at 0. https://arxiv.org/abs/2001.04337

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