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

2017/09/28 by Jenkins, Paul, Keck, Ryan, Moss, Eric
#11F30 #11F37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1709.10189

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 ∞.

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