Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A reciprocity law for certain Frobenius extensions

Author(s): Yuanli Zhang
Journal: Proc. Amer. Math. Soc. 124 (1996), 1643-1648.
MSC (1991): Primary 11F39, 11R80, 11F70
MathSciNet review: 1350967
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Abstract: Let $E/F$ be a finite Galois extension of algebraic number fields with Galois group $G$ . Assume that $G$ is a Frobenius group and $H$ is a Frobenius complement of $G$ . Let $F(H)$ be the maximal normal nilpotent subgroup of $H$ . If $H/F(H)$ is nilpotent, then every Artin L-function attached to an irreducible representation of $G$ arises from an automorphic representation over $F$ , i.e., the Langlands' reciprocity conjecture is true for such Galois extensions.

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