Generalised form of a conjecture of Jacquet and a local consequence
| dc.creator | Prasad, Dipendra | |
| dc.creator | Schulze-Pillot, Rainer | |
| dc.date | 2006-06-21 | |
| dc.date | 2007-06-17 | |
| dc.date.accessioned | 2026-07-07T08:10:20Z | |
| dc.date.available | 2026-07-07T08:10:20Z | |
| dc.description | Following the work of Harris and Kudla we prove a more general form of a conjecture of Jacquet relating the non-vanishing of a certain period integral to non-vanishing of the central critical value of a certain $L$-function. As a consequence we deduce certain local results about the existence of $GL_2(k)$-invariant linear forms on irreducible, admissible representations of $GL_2({\Bbb K})$ for ${\Bbb K}$ a commutative semi-simple cubic algebra over a non-archimedean local field $k$ in terms of certain local epsilon factors which were proved only in certain cases by the first author in his earlier work. This has been achieved by globalising a locally distinguished representation to a globally distinguished representation, a result of independent interest. | |
| dc.description | 20 pages. Typos corrected and some minor changes. To appear in Journal fuer die Reine und Angewandte Mathematik | |
| dc.identifier | https://arxiv.org/abs/math/0606515 | |
| dc.identifier | http://arxiv.org/abs/math/0606515 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131796 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 11F70; 22E55; 22E50 | |
| dc.title | Generalised form of a conjecture of Jacquet and a local consequence | |
| dc.type | text |