L-functions of symmetric powers of cubic exponential sums

dc.creatorHaessig, C. Douglas
dc.date2006-08-21
dc.date2008-01-09
dc.date.accessioned2026-07-07T08:53:21Z
dc.date.available2026-07-07T08:53:21Z
dc.descriptionFor 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.descriptionImplemented changes suggested by referee. Fixed typos and improved exposition of some sections. Proof of Conjecture 3.1 given. 38 pages
dc.identifierhttps://arxiv.org/abs/math/0608521
dc.identifierhttp://arxiv.org/abs/math/0608521
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145594
dc.subjectNumber Theory
dc.subject11L03
dc.titleL-functions of symmetric powers of cubic exponential sums
dc.typetext

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