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The modular equation and modular forms of weight one

Published online by Cambridge University Press:  22 January 2016

Toyokazu Hiramatsu  and
Yoshio Mimura
Toyokazu Hiramatsu
Affiliation:
Department of Mathematics Kobe University, Rokko, Kobe, 657, Japan
Yoshio Mimura
Affiliation:
Department of Mathematics Kobe University, Rokko, Kobe, 657, Japan
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This is a continuation of the previous paper [8] concerning the relation between the arithmetic of imaginary quadratic fields and cusp forms of weight one on a certain congruence subgroup. Let K be an imaginary quadratic field, say K = with a prime number q ≡ − 1 mod 8, and let h be the class number of K. By the classical theory of complex multiplication, the Hubert class field L of K can be generated by any one of the class invariants over K, which is necessarily an algebraic integer, and a defining equation of which is denoted by

Φ(x) = 0.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 100 , December 1985 , pp. 145 - 162
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

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