On the special values of certain Rankin-Selberg L-functions and applications to odd symmetric power L-functions of modular forms
| dc.creator | Raghuram, A. | |
| dc.date | 2008-11-26 | |
| dc.date.accessioned | 2026-07-07T12:06:07Z | |
| dc.date.available | 2026-07-07T12:06:07Z | |
| dc.description | We prove an algebraicity result for the central critical value of certain Rankin-Selberg L-functions for GL(n) x GL(n-1). This is a generalization and refinement of some results of Harder, Kazhdan-Mazur-Schmidt, Mahnkopf, and Kasten-Schmidt. As an application of this result, we prove algebraicity results for certain critical values of the fifth and the seventh symmetric power L-functions attached to a holomorphic cusp form. Assuming Langlands functoriality one can prove similar algebraicity results for the special values of any odd symmetric power L-function. We also prove a conjecture of Blasius and Panchishkin on twisted L-values in some cases. We comment on the compatibility of our results with Deligne's conjecture on the critical values of motivic L-functions. These results, as in the above mentioned works, are, in general, based on a nonvanishing hypothesis on certain archimedean integrals. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/0811.4435 | |
| dc.identifier | http://arxiv.org/abs/0811.4435 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208564 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 11F67; 11F70, 11F75, 22E55 | |
| dc.title | On the special values of certain Rankin-Selberg L-functions and applications to odd symmetric power L-functions of modular forms | |
| dc.type | text |