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Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs
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Shuichiro Takeda
Published/Copyright:
March 10, 2011
Abstract
Following the approach of B. Roberts, we characterize the non-vanishing of the global theta lift for symplectic-orthogonal dual pairs in terms of its local counterpart. In particular, we replace the temperedness assumption present in Robert's work by a certain weaker assumption, and apply our results to small rank similitude groups. Among our applications is a certain instance of Langlands functorial transfer of a (non-generic) cuspidal automorphic representation of GSp(4) to GL(4).
Received: 2008-12-11
Revised: 2010-04-20
Published Online: 2011-03-10
Published in Print: 2011-August
© Walter de Gruyter Berlin · New York 2011
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Articles in the same Issue
- Coefficients and non-triviality of the Jones polynomial
- Distribution of algebraic numbers
- Some local-global non-vanishing results of theta lifts for symplectic-orthogonal dual pairs
- Characterizing quaternion rings over an arbitrary base
- Transcendence in positive characteristic and special values of hypergeometric functions
- Factoring 3-fold flips and divisorial contractions to curves
- Existence of permanent and breaking waves for the periodic Degasperis–Procesi equation with linear dispersion
- -actions on UHF algebras of infinite type
