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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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| _version_ | 1866917993110306816 |
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| author | Feigon, Brooke Martin, Kimball Whitehouse, David |
| author_facet | Feigon, Brooke Martin, Kimball Whitehouse, David |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1308_2253 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Periods and nonvanishing of central L-values for GL(2n) Feigon, Brooke Martin, Kimball Whitehouse, David Number Theory Representation Theory 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. |
| title | Periods and nonvanishing of central L-values for GL(2n) |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/1308.2253 |