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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Strong multiplicity theorems for $ {\rm GL}(n)$


Author: George T. Gilbert
Journal: Trans. Amer. Math. Soc. 302 (1987), 561-576
MSC: Primary 11F70; Secondary 22E55
MathSciNet review: 891635
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Abstract: Let $ \pi = \otimes {\pi _\upsilon }$ be a cuspidal automorphic representation of $ GL(n,{F_A})$, where $ {F_A}$ denotes the adeles of a number field $ F$. Let $ E$ be a Galois extension of $ F$ and let $ \{ g\} $ denote a conjugacy class of the Galois group. The author considers those cuspidal automorphic representations which have local components $ {\pi _\upsilon }$ whenever the Frobenius of the prime $ \upsilon$ is $ \{ g\} $, showing that such representations are often easily described and finite in number. This generalizes a result of Moreno [Bull. Amer. Math. Soc. 11 (1984), pp. 180-182].


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0891635-9
PII: S 0002-9947(1987)0891635-9
Article copyright: © Copyright 1987 American Mathematical Society