Modular Counting of Rational Points over Finite Fields

被引：0
|
作者：
Daqing Wan
机构：
[1] Department of Mathematics,
[2] University of California,undefined
来源：
Foundations of Computational Mathematics | 2008年 / 8卷
关键词：
Zeta Function; Rational Point; Finite Field; Polynomial Time Algorithm; Newton Polygon;
D O I：
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摘要：
Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m nonzero terms. Let N(f) denote the number of solutions of f(x) = 0 with coordinates in Fq. In this paper we give a deterministic algorithm which computes the reduction of N(f) modulo pb in O(n(8m)p(h+b)p) bit operations. This is singly exponential in each of the parameters {h, b, p}, answering affirmatively an open problem proposed by Gopalan, Guruswami, and Lipton.
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页码：597 / 605
页数：8
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