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On the factorization of the discriminant of a classical modular equation

Volume 178 / 2017

Mitsusada Nakata Acta Arithmetica 178 (2017), 77-85 MSC: Primary 11F03; Secondary 12D05, 14K22. DOI: 10.4064/aa8538-8-2016 Published online: 30 January 2017

Abstract

This paper is concerned with the discriminant of a classical modular equation of prime level. Weber determined all its factors but not their multiplicities. This paper fills in that gap by presenting an explicit formula for the discriminant and its factors with multiplicities. Also a relation between a classical modular equation of prime level $p$ and that of level $p^2$ is presented.

Authors

  • Mitsusada Nakata9-2-5, Karita, Sumiyoshi-ku
    Osaka-shi, Osaka, Japan
    e-mail

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