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L-functions of Exponential sums over one-dimensional affinoid: Newton over Hodge | | Hui June Zhu
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8 Feb 2003 | | Journal: | Inter. Math. Research Notices, 2004, no. 30, (2004), 1529--1550 | | Subject: | Number Theory; Algebraic Geometry MSC-class: 11,14 | math.NT math.AG | | Abstract: | Let p be a prime and let F_pbar be the algebraic closure of the finite field of p elements. Let f(x) be any one variable rational function over F_pbar with n poles of orders d_1, ...,d_n. Suppose p is coprime to d_i for every i. We prove that there exists a Hodge polygon, depending only on d_i’s, which is a lower bound to the Newton polygon of L functions of exponential sums of f(x). Moreover, we show that these two polygons coincide if p=1 mod d_i for every i=1,...,n. As a corollary, we obtain a tight lower bound of Newton polygon of Artin-Schreier curve. | | Source: | arXiv, math.NT/0302085 | | Services: | Forum | Review | PDF | Favorites | |
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