On Shalika Periods and a Theorem of Jacquet-Martin
| dc.creator | Gan, Wee Teck | |
| dc.creator | Takeda, Shuichiro | |
| dc.date | 2007-05-11 | |
| dc.date | 2008-05-18 | |
| dc.date.accessioned | 2026-07-07T09:39:12Z | |
| dc.date.available | 2026-07-07T09:39:12Z | |
| dc.description | Let πbe a cuspidal automorphic representation of GL_4 with central character μ^2. It is known that πhas Shalika period with respect to μif and only if the L-function L^S(s, π, \bigwedge^2\otimesμ^{-1}) has a pole at s=1. Recentlt, Jacquet and Martin considered the analogous question for cuspidal representations π_D of the inner form GL_2(D)(\A), and obtained a partial result via the relative trace formula. In this paper, we provide a complete solution to this problem via the method of theta correspondence, and give necessary and sufficient conditions for the existence of Shalika period for π_D. We also resolve the analogous question in the local setting. | |
| dc.identifier | https://arxiv.org/abs/0705.1576 | |
| dc.identifier | http://arxiv.org/abs/0705.1576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161082 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.title | On Shalika Periods and a Theorem of Jacquet-Martin | |
| dc.type | text |