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L-functions of symmetric powers of cubic exponential sums
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C. Douglas Haessig
Published/Copyright:
March 31, 2009
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 x3 + λx where λ runs over 
. 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.
Received: 2007-08-28
Revised: 2008-01-09
Published Online: 2009-03-31
Published in Print: 2009-June
© Walter de Gruyter Berlin · New York 2009
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- L-functions of symmetric powers of cubic exponential sums
- Localization in quiver moduli
- Kolyvagin systems of Stark units
- Overconvergence and classicality: the case of curves
- Partial sums of the Möbius function
- Gram determinants and semisimplicity criteria for Birman-Wenzl algebras
- Degeneration of the strange duality map for symplectic bundles
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Articles in the same Issue
- L-functions of symmetric powers of cubic exponential sums
- Localization in quiver moduli
- Kolyvagin systems of Stark units
- Overconvergence and classicality: the case of curves
- Partial sums of the Möbius function
- Gram determinants and semisimplicity criteria for Birman-Wenzl algebras
- Degeneration of the strange duality map for symplectic bundles
- Fubini's theorem in codimension two
