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

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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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  1. Department of Mathematics, Dongguk University-Seoul, 30 Pildong-ro 1-gil, Jung-gu, Seoul, 04620, Republic of Korea

    Bumkyu Cho

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  1. Bumkyu Cho
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Correspondence to Bumkyu Cho.

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The author was supported by NRF-2018R1A2B6001645 and the Dongguk University Research Fund of 2018.

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Cho, B. Modular equations for congruence subgroups of genus zero. Ramanujan J 51, 187–204 (2020). https://doi.org/10.1007/s11139-018-0116-6

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  • DOI: https://doi.org/10.1007/s11139-018-0116-6

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