Cusp forms of weight one, quartic reciprocity and elliptic curves

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 D 4 of order 8 and has the unique two-dimensional irreducible complex representation ψ. In view of the theory of Hecke-Weil-Lan...

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Bibliographic Details
Published in:Nagoya mathematical journal 1985-01, Vol.98, p.117-137
Main Author: Ishii, Noburo
Format: Article
Language:English
Subjects:
11F12
11F80
11R42
14G10
14K07
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Summary: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 D 4 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]).
ISSN:0027-7630
2152-6842
DOI:10.1017/S0027763000021413