Translator Disclaimer
October, 2020 Recurrence Relations Satisfied by the Traces of Singular Moduli for $\Gamma_0(N)$
Bumkyu Cho
Taiwanese J. Math. 24(5): 1045-1072 (October, 2020). DOI: 10.11650/tjm/200202

Abstract

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

Citation

Download Citation

Bumkyu Cho. "Recurrence Relations Satisfied by the Traces of Singular Moduli for $\Gamma_0(N)$." Taiwanese J. Math. 24 (5) 1045 - 1072, October, 2020. https://doi.org/10.11650/tjm/200202

Information

Received: 20 March 2019; Revised: 25 January 2020; Accepted: 5 February 2020; Published: October, 2020
First available in Project Euclid: 12 February 2020

MathSciNet: MR4152655
Digital Object Identifier: 10.11650/tjm/200202

Subjects:
Primary: 11F03

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
28 PAGES


SHARE
Vol.24 • No. 5 • October, 2020
Back to Top