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arXiv · 2002.02409

Recurrence relations satisfied by the traces of singular moduli for $\Gamma_0(N)$

Bumkyu Cho
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Abstract

We compute the divisor of the modular equation on the modular curve $\Gamma_0(N) \backslash \mathbb H^*$ and then find recurrence relations satisfied by the modular traces of the Hauptmodul for any congruence subgroup $\Gamma_0(N)$ of genus zero. We also introduce the notions and properties of $\Gamma$-equivalence and $\Gamma$-reduced forms about binary quadratic forms. Using these, we can explicitly compute the recurrence relations for $N = 2, 3, 4, 5$.

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Bumkyu Cho. 2020-02-05. Recurrence relations satisfied by the traces of singular moduli for $\Gamma_0(N)$. https://arxiv.org/abs/2002.02409

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