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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1308.2253 |
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Table of Contents:
- Let $π$ be a cuspidal automorphic representation of PGL($2n$) over a number field $F$, and $η$ the quadratic idele class character attached to a quadratic extension $E/F$. Guo and Jacquet conjectured a relation between the nonvanishing of $L(1/2,π)L(1/2, π\otimes η)$ for $π$ of symplectic type and the nonvanishing of certain GL($n,E$) periods. When $n=1$, this specializes to a well-known result of Waldspurger. We prove this conjecture, and related global results, under some local hypotheses using a simple relative trace formula. We then apply these global results to obtain local results on distinguished supercuspidal representations, which partially establish a conjecture of Prasad and Takloo-Bighash.