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Newton polygons for L-functions of generalized Kloosterman sums.
- Source :
-
Forum Mathematicum . Jan2022, Vol. 34 Issue 1, p77-96. 20p. - Publication Year :
- 2022
-
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 F ¯ (λ ¯ , x) := ∑ i = 1 n x i a i + λ ¯ ∏ i = 1 n x i - 1 , \bar{F}(\bar{\lambda},x):=\sum_{i=1}^{n}x_{i}^{a_{i}}+\bar{\lambda}\prod_{i=1}% ^{n}x_{i}^{-1}, with a 1 , ... , a n {a_{1},\ldots,a_{n}} being pairwise coprime for n ≥ 2 {n\geq 2}. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NEWTON diagrams
*L-functions
*POLYGONS
*NEWTON-Raphson method
Subjects
Details
- Language :
- English
- ISSN :
- 09337741
- Volume :
- 34
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Forum Mathematicum
- Publication Type :
- Academic Journal
- Accession number :
- 154830441
- Full Text :
- https://doi.org/10.1515/forum-2021-0220