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Modular equations for congruence subgroups of genus zero

  • Bumkyu ChoEmail author
Article
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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 \(\varGamma _1(m) \cap \varGamma _0(mN)\) of genus zero satisfies similar properties including Kronecker’s congruence relation.

Keywords

Modular equations Modular polynomials Kronecker’s congruence relation 

Mathematics Subject Classification

11F03 

Notes

Acknowledgements

The author would like to express his sincere thanks to the anonymous referee for a careful reading of the manuscript.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsDongguk University-SeoulSeoulRepublic of Korea

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