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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Strong multiplicity theorems for $\textrm {GL}(n)$
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by George T. Gilbert PDF
Trans. Amer. Math. Soc. 302 (1987), 561-576 Request permission

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].
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 561-576
  • MSC: Primary 11F70; Secondary 22E55
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0891635-9
  • MathSciNet review: 891635