On certain period relations for cusp forms on GL_n
| dc.creator | Raghuram, A. | |
| dc.creator | Shahidi, Freydoon | |
| dc.date | 2007-07-11 | |
| dc.date.accessioned | 2026-07-07T08:16:11Z | |
| dc.date.available | 2026-07-07T08:16:11Z | |
| dc.description | Let $π$ be a regular algebraic cuspidal automorphic representation of ${\rm GL}_n({\mathbb A}_F)$ for a number field $F$. We consider certain periods attached to $π$. These periods were originally defined by Harder when $n=2$, and later by Mahnkopf when $F = {\mathbb Q}$. In the first part of the paper we analyze the behaviour of these periods upon twisting $π$ by algebraic Hecke characters. In the latter part of the paper we consider Shimura's periods associated to a modular form. If $ϕ_χ$ is the cusp form associated to a character $χ$ of a quadratic extension, then we relate the periods of $ϕ_{χ^n}$ to those of $ϕ_χ$, and as a consequence give another proof of Deligne's conjecture on the critical values of symmetric power $L$-functions associated to dihedral modular forms. Finally, we make some remarks on the symmetric fourth power $L$-functions. | |
| dc.description | 40 pages. This preprint is also up on preprint server of the Erwin Schrodinger Institute as preprint number 1928. The URL is http://www.esi.ac.at/Preprint-shadows/esi1928.html | |
| dc.identifier | https://arxiv.org/abs/0707.1708 | |
| dc.identifier | http://arxiv.org/abs/0707.1708 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133694 | |
| dc.subject | Number Theory | |
| dc.subject | Representation Theory | |
| dc.subject | 11F67; 11F70, 22E55 | |
| dc.title | On certain period relations for cusp forms on GL_n | |
| dc.type | text |