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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A reciprocity law
for certain Frobenius extensions


Author: 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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Additional Information

Yuanli Zhang
Affiliation: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720
Address at time of publication: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: yuanli@msri.org, yz@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03603-9
PII: S 0002-9939(96)03603-9
Received by editor(s): October 5, 1994
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1996 American Mathematical Society