A reciprocity law for certain Frobenius extensions

Zhang, Yuanli

doi:10.1090/S0002-9939-96-03603-9

A reciprocity law for certain Frobenius extensions
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Proc. Amer. Math. Soc. 124 (1996), 1643-1648 Request permission

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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