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- W2510132618 abstract "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 + lambda x. 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." @default.
- W2510132618 created "2016-09-16" @default.
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- W2510132618 date "2006-08-21" @default.
- W2510132618 modified "2023-09-26" @default.
- W2510132618 title "On the Symmetric Powers of the $p$-adic Airy family" @default.
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