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Higher reciprocity law, modular forms of weight 1 and elliptic curves

Published online by Cambridge University Press:  22 January 2016

Masao Koike
Masao Koike*
Affiliation:
Department of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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In this paper, we study higher reciprocity law of irreducible polynomials f(x) over Q of degree 3, especially, its close connection with elliptic curves rational over Q and cusp forms of weight 1. These topics were already studied separately in a special example by Chowla-Cowles [1] and Hiramatsu [2]. Here we bring these objects into unity.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 98 , June 1985 , pp. 109 - 115
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[ 1 ] Chowla, S. and Cowles, M., On the coefficients cn in the expansion J. reine angew. Math., 292 (1977), 115–116.Google Scholar
[ 2 ] Hiramatsu, T., Higher reciprocity law and modular forms of weight one, Comm. Math. Univ. St. Paul, 31 (1982), 75–85.Google Scholar
[ 3 ] Hiramatsu, T. and Mimura, Y., The modular equation and modular forms of weight one, preprint.Google Scholar
[ 4 ] Hiramatsu, T., Ishii, N. and Mimura, Y., On indefinite modular forms of weight one, preprint.Google Scholar
[ 5 ] Moreno, C., The higher reciprocity law: an example, J. Number Theory, 12 (1980), 57–70.Google Scholar