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A strengthening of the GL(2) converse theorem

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  07 February 2011

Andrew R. Booker  and
M. Krishnamurthy
Andrew R. Booker
Affiliation:
School of Mathematics, Bristol University, University Walk, Bristol, BS8 1TW, UK (email: [email protected])
M. Krishnamurthy
Affiliation:
Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA (email: [email protected])
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Abstract

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We generalize the method of A. R. Booker (Poles of Artin L-functions and the strong Artin conjecture, Ann. of Math. (2) 158 (2003), 1089–1098; MR 2031863(2004k:11082)) to prove a version of the converse theorem of Jacquet and Langlands with relaxed conditions on the twists by ramified idèle class characters.

Keywords

converse theoremautomorphic forms

MSC classification

Secondary: 11F41: Automorphic forms on $(2)$; Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 3 , May 2011 , pp. 669 - 715
Copyright
Copyright © Foundation Compositio Mathematica 2011

References

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