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Isolating Rankin-Selberg lifts

Authors: Jayce R. Getz and Jamie Klassen
Journal: Proc. Amer. Math. Soc. 143 (2015), 3319-3329
MSC (2010): Primary 11F66; Secondary 20G05
Published electronically: April 6, 2015
MathSciNet review: 3348774
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Abstract: Let $ F$ be a number field and let $ \pi $ be a cuspidal unitary automorphic representation of $ \mathrm {GL}_{mn}(\mathbb{A}_F)$ where $ m$ and $ n$ are integers greater than one. We propose a conjecturally necessary condition for $ \pi $ to be a Rankin-Selberg transfer of an automorphic representation of $ \mathrm {GL}_m \times \mathrm {GL}_n(\mathbb{A}_F)$. As evidence for the conjecture we prove the corresponding statement about automorphic $ L$-parameters.

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Additional Information

Jayce R. Getz
Affiliation: Department of Mathematics, Duke University, Durham, North Carolina 27708-0320

Jamie Klassen
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 0B9

Received by editor(s): February 26, 2013
Received by editor(s) in revised form: July 4, 2013, and October 18, 2013
Published electronically: April 6, 2015
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2015 American Mathematical Society

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