Modular equations for congruence subgroups of genus zero

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Abstract

It is well known that the modular equation for the full modular group satisfies several properties such as Kronecker’s congruence relation. In this article, we prove that the modular equation for any congruence subgroup Γ1(m) ∩ Γ(mN) of genus zero satisfies similar properties including Kronecker’s congruence relation.

Original languageEnglish
Pages (from-to)187-204
Number of pages18
JournalRamanujan Journal
Volume51
Issue number1
DOIs
StatePublished - 1 Jan 2020

Keywords

  • Kronecker’s congruence relation
  • Modular equations
  • Modular polynomials

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