Taiwanese Journal of Mathematics

Recurrence Relations Satisfied by the Traces of Singular Moduli for $\Gamma_0(N)$

Bumkyu Cho

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We compute the divisor of the modular equation on the modular curve $\Gamma_0(N) \setminus \mathbb{H}^*$ 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 $N = 2,3,4,5$.

Article information

Taiwanese J. Math., Advance publication (2020), 28 pages.

First available in Project Euclid: 12 February 2020

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Digital Object Identifier

Primary: 11F03: Modular and automorphic functions

traces of singular moduli $\Gamma$-equivalence $\Gamma$-reduced forms


Cho, Bumkyu. Recurrence Relations Satisfied by the Traces of Singular Moduli for $\Gamma_0(N)$. Taiwanese J. Math., advance publication, 12 February 2020. doi:10.11650/tjm/200202. https://projecteuclid.org/euclid.twjm/1581476420

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