L-functions of symmetric powers of cubic exponential sums
| dc.creator | Haessig, C. Douglas | |
| dc.date | 2006-08-21 | |
| dc.date | 2008-01-09 | |
| dc.date.accessioned | 2026-07-07T08:53:21Z | |
| dc.date.available | 2026-07-07T08:53:21Z | |
| dc.description | For each positive integer k, we investigate the L-function attached to the k-th symmetric power of the F-crystal associated to the family of cubic exponential sums of x^3 + λx. We explore its rationality, field of definition, degree, trivial factors, functional equation, and Newton polygon. The paper is essentially self-contained, due to the remarkable and attractive nature of Dwork's p-adic theory. A novel feature of this paper is an extension of Dwork's effective decomposition theory when k < p. This allows for explicit computations in the associated p-adic cohomology. In particular, the action of Frobenius on the (primitive) cohomology spaces may be explicitly studied. | |
| dc.description | Implemented changes suggested by referee. Fixed typos and improved exposition of some sections. Proof of Conjecture 3.1 given. 38 pages | |
| dc.identifier | https://arxiv.org/abs/math/0608521 | |
| dc.identifier | http://arxiv.org/abs/math/0608521 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145594 | |
| dc.subject | Number Theory | |
| dc.subject | 11L03 | |
| dc.title | L-functions of symmetric powers of cubic exponential sums | |
| dc.type | text |