Recurrence relations satisfied by the traces of singular moduli for Γ0 (n)

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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 languageEnglish
Pages (from-to)1045-1072
Number of pages28
JournalTaiwanese Journal of Mathematics
Volume24
Issue number5
DOIs
StatePublished - Oct 2020

Keywords

  • Traces of singular moduli
  • Γ-equivalence
  • Γ-reduced forms

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