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arXiv · 1711.06239

Divisibility properties of coefficients of modular functions in genus zero levels

Victoria Iba·Paul Jenkins·Merrill Warnick
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Abstract

We prove divisibility results for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight $0$ and levels $6, 10, 12, 18$ with poles only at the cusp at infinity. In addition, we show that these Fourier coefficients satisfy Zagier duality in all weights, and give a general formula for the generating functions of such canonical bases for all genus zero levels.

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Victoria Iba, Paul Jenkins, Merrill Warnick. 2018-07-27. Divisibility properties of coefficients of modular functions in genus zero levels. https://arxiv.org/abs/1711.06239

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