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A Functional Equation for Degree two Local Factors

Published online by Cambridge University Press:  20 November 2018

Paul Gérardin  and
Wen-Ch'ing Winnie Li
Paul Gérardin
Affiliation:
U.E.R. de Mathématique et, Informatique, Université Paris VII 2, Place Jussieu, 75251 Paris Cedex 5, France and Department of Mathematics, Pennsylvania State University, University Park, PA 16802, U.S.A.
Wen-Ch'ing Winnie Li
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, U.S.A.
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Abstract

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We show that the Fourier transforms of the admissible irreducible representations of the group GL2 over a nonarchimedian local field F are characterized by a functional equation (MF). We also prove that the functions satisfying (MF) and having at most one pole are exactly the Fourier transforms of the irreducible representations of the quaternion group H over F. The Jacquet-Langlands correspondence between irreducible representations of H and discrete series of GL2 then follows immediately from our criteria.

Keywords

12B2712B30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 3 , 01 September 1985 , pp. 355 - 371
Copyright
Copyright © Canadian Mathematical Society 1985

References

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