Abstract
We compute the divisor of the modular equation on the modular curve Γ0 (N) \ ℍ∗ and then find recurrence relations satisfied by the modular traces of the Hauptmodul for any congruence subgroup Γ0 (N) of genus zero. We also intro-duce the notions and properties of Γ-equivalence and Γ-reduced forms about binary quadratic forms. Using these, we can explicitly compute the recurrence relations for N = 2, 3, 4, 5.
Original language | English |
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Pages (from-to) | 1045-1072 |
Number of pages | 28 |
Journal | Taiwanese Journal of Mathematics |
Volume | 24 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2020 |
Keywords
- Traces of singular moduli
- Γ-equivalence
- Γ-reduced forms