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

Bumkyu Cho

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

Number Theory 2020-02-07 v1

Authors: Bumkyu Cho

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 $N = 2, 3, 4, 5$ .

Keywords

singular moduli modular traces gamma_0(n) recurrence relations hauptmodul binary quadratic forms

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@article{arxiv.2002.02409,
  title  = {Recurrence relations satisfied by the traces of singular moduli for $\Gamma_0(N)$},
  author = {Bumkyu Cho},
  journal= {arXiv preprint arXiv:2002.02409},
  year   = {2020}
}

Comments

Accepted for publication in the Taiwanese Journal of Mathematics. arXiv admin note: text overlap with arXiv:1711.00230

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

Abstract

Keywords

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