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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Some local-global non-vanishing results for theta lifts from orthogonal groups
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by Shuichiro Takeda PDF
Trans. Amer. Math. Soc. 361 (2009), 5575-5599 Request permission

Abstract:

We, first, improve a theorem of B. Roberts which characterizes non-vanishing of a global theta lift from $\operatorname {O}(X)$ to $\operatorname {Sp}(n)$ in terms of non-vanishing of local theta lifts. In particular, we will remove all the Archimedean conditions imposed upon his theorem. Secondly, following Roberts, we will apply our theorem to theta lifting of low rank similitude groups. Namely we characterize the non-vanishing condition of a global theta lift from $\operatorname {GO}(4)$ to $\operatorname {GSp}(2)$ in our improved setting. Also we consider non-vanishing conditions of a global theta lift from $\operatorname {GO}(4)$ to $\operatorname {GSp}(1)$ and explicitly compute the lift when it exists.
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Additional Information
  • Shuichiro Takeda
  • Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd St., Philadelphia, Pennsylvania 19104-6395
  • Address at time of publication: Department of Mathematics, Purdue University, 150 N. University, West Lafayette, Indiana 47907
  • MR Author ID: 873141
  • Email: stakeda@math.upenn.edu, stakeda@math.purdue.edu
  • Received by editor(s): July 31, 2006
  • Received by editor(s) in revised form: January 22, 2008
  • Published electronically: April 10, 2009
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 5575-5599
  • MSC (2000): Primary 11F27
  • DOI: https://doi.org/10.1090/S0002-9947-09-04787-4
  • MathSciNet review: 2515824