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Cusp forms of weight one, quartic reciprocity and elliptic curves

Published online by Cambridge University Press:  22 January 2016

Noburo Ishii
Noburo Ishii*
Affiliation:
Department of Mathematics, University of Osaka Prefecture, Sakai, Osaka 591, Japan
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Let m be a non-square positive integer. Let K be the Galois extension over the rational number field Q generated by and . Then its Galois group over Q is the dihedral group D4 of order 8 and has the unique two-dimensional irreducible complex representation ψ. In view of the theory of Hecke-Weil-Langlands, we know that ψ defines a cusp form of weight one (cf. Serre [6]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 98 , June 1985 , pp. 117 - 137
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

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