Modular equations for congruence subgroups of genus zero
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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 \(\varGamma _1(m) \cap \varGamma _0(mN)\) of genus zero satisfies similar properties including Kronecker’s congruence relation.
KeywordsModular equations Modular polynomials Kronecker’s congruence relation
Mathematics Subject Classification11F03
The author would like to express his sincere thanks to the anonymous referee for a careful reading of the manuscript.
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