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Periods and nonvanishing of central L-values for GL(2n)
- Source :
- Israel Journal of Mathematics. 225:223-266
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- Let $\pi$ be a cuspidal automorphic representation of PGL($2n$) over a number field $F$, and $\eta$ the quadratic idele class character attached to a quadratic extension $E/F$. Guo and Jacquet conjectured a relation between the nonvanishing of $L(1/2,\pi)L(1/2, \pi \otimes \eta)$ for $\pi$ 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.<br />Comment: 31 pages; to appear in Israel J. Math
- Subjects :
- Pure mathematics
Trace (linear algebra)
Conjecture
Mathematics - Number Theory
Mathematics::Number Theory
General Mathematics
010102 general mathematics
Type (model theory)
Algebraic number field
01 natural sciences
Character (mathematics)
Quadratic equation
Simple (abstract algebra)
0103 physical sciences
FOS: Mathematics
Number Theory (math.NT)
010307 mathematical physics
Representation Theory (math.RT)
0101 mathematics
Mathematics::Representation Theory
Mathematics - Representation Theory
Mathematics
Symplectic geometry
Subjects
Details
- ISSN :
- 15658511 and 00212172
- Volume :
- 225
- Database :
- OpenAIRE
- Journal :
- Israel Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....c15dd8c5a24902d8cf2a281f374b86a8