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A Relation between Automorphic Forms on GL(2) and GL(3)

Stephen Gelbart and Hervé Jacquet
Proceedings of the National Academy of Sciences of the United States of America
Vol. 73, No. 10 (Oct., 1976), pp. 3348-3350
Stable URL: http://www.jstor.org/stable/66594
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Relation between Automorphic Forms on GL(2) and GL(3)
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Abstract

Let ρ n denote the standard n-dimensional representation of GL(n,C) and ρ n 2 its symmetric square. For each automorphic cuspidal representation π of GL(2,A) we introduce an Euler product L(s,π ,ρ 2 2) of degree 3 which we prove is entire. We also prove that there exists an automorphic representation Π of GL(3)-``the lift of π ''-with the property that L(s,Π ,ρ 3) = L(s,π ,ρ 2 2). Our results confirm conjectures described in a more general context by R. P. Langlands [(1970) Lecture Notes in Mathematics, no. 170 (Springer-Verlag, Berlin-Heidelberg-New York)].

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