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arXiv · 1504.07364

Generators of the ring of weakly holomorphic modular functions for $\Gamma_1(N)$

Ja Kyung Koo·Dong Sung Yoon
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Abstract

For a positive integer $N$ divisible by $4,5,6,7$ or $9$, let $\mathcal{O}_{1,N}(\mathbb{Q})$ be the ring of weakly holomorphic modular functions for the congruence subgroup $\Gamma_1(N)$ with rational Fourier coefficients. We present explicit generators of the ring $\mathcal{O}_{1,N}(\mathbb{Q})$ over $\mathbb{Q}$ by making use of modular units which have infinite product expansions.

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Ja Kyung Koo, Dong Sung Yoon. 2015-04-28. Generators of the ring of weakly holomorphic modular functions for $\Gamma_1(N)$. https://arxiv.org/abs/1504.07364

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