Newton polygons for L-functions of generalized Kloosterman sums
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Chunlin Wang
Abstract
In the present paper, we study the Newton polygons for the L-functions of n-variable generalized Kloosterman sums. Generally, the Newton polygon has a topological lower bound, called the Hodge polygon. In order to determine the Hodge polygon, we explicitly construct a basis of the top-dimensional Dwork cohomology. Using Wan’s decomposition theorem and diagonal local theory, we obtain when the Newton polygon coincides with the Hodge polygon. In particular, we concretely get the slope sequence for the L-function of
with
Funding source: Beijing Postdoctoral Science Foundation
Award Identifier / Grant number: 2020ZZ073
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11901415
Funding source: China Scholarship Council
Award Identifier / Grant number: 201808515110
Funding statement: L. P. Yang is supported by Beijing Postdoctoral Research Foundation (No. 2020ZZ073). C. L. Wang is supported by National Natural Science Foundation of China (No. 11901415) and the China Scholarship Council (No. 201808515110).
Acknowledgements
We wish to thank Steven Sperber for suggesting the subject considered in this paper, and Daqing Wan for much helpful advice. We also would like to thank the referee for his/her careful reading and very helpful comments of the manuscript. Liping Yang would like to thank Liman Chen, Huaiqian Li and Hao Zhang for many helpful discussions.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Contramodules over pro-perfect topological rings
- Multigraded Castelnuovo–Mumford regularity via Klyachko filtrations
- Resistance scaling on 4N-carpets
- Newton polygons for L-functions of generalized Kloosterman sums
- Embeddings of locally compact abelian p-groups in Hawaiian groups
- A theorem of Roe and Strichartz on homogeneous trees
- Hankel determinants for starlike and convex functions associated with sigmoid functions
- Modular iterated integrals associated with cusp forms
- Calderón–Zygmund operators on multiparameter Lipschitz spaces of homogeneous type
- Gompf connected sum for orbifolds and K-contact Smale–Barden manifolds
- Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces
Artikel in diesem Heft
- Frontmatter
- Contramodules over pro-perfect topological rings
- Multigraded Castelnuovo–Mumford regularity via Klyachko filtrations
- Resistance scaling on 4N-carpets
- Newton polygons for L-functions of generalized Kloosterman sums
- Embeddings of locally compact abelian p-groups in Hawaiian groups
- A theorem of Roe and Strichartz on homogeneous trees
- Hankel determinants for starlike and convex functions associated with sigmoid functions
- Modular iterated integrals associated with cusp forms
- Calderón–Zygmund operators on multiparameter Lipschitz spaces of homogeneous type
- Gompf connected sum for orbifolds and K-contact Smale–Barden manifolds
- Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces
