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arXiv · 1501.04193

Determination of the Fricke families

Ick Sun Eum·Dong Hwa Shin
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Abstract

For a positive integer $N$ divisible by $4$, let $\mathcal{O}^1_N(\mathbb{Q})$ be the ring of weakly holomorphic modular functions for the congruence subgroup $Γ^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring $\mathcal{O}^1_N(\mathbb{Q})$ over $\mathbb{Q}$, from which we are able to classify all Fricke families of such level $N$.

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Ick Sun Eum, Dong Hwa Shin. 2015-09-23. Determination of the Fricke families. https://arxiv.org/abs/1501.04193

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