L-functions of Exponential sums over one-dimensional affinoid: Newton over Hodge
| dc.creator | Zhu, Hui June | |
| dc.date | 2003-02-08 | |
| dc.date | 2005-02-01 | |
| dc.date.accessioned | 2026-07-07T04:55:06Z | |
| dc.date.available | 2026-07-07T04:55:06Z | |
| dc.description | 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. | |
| dc.description | 17 pages, LaTEX | |
| dc.identifier | https://arxiv.org/abs/math/0302085 | |
| dc.identifier | http://arxiv.org/abs/math/0302085 | |
| dc.identifier | Inter. Math. Research Notices, 2004, no. 30, (2004), 1529--1550 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66472 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11,14 | |
| dc.title | L-functions of Exponential sums over one-dimensional affinoid: Newton over Hodge | |
| dc.type | text |