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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：
暂无
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学科分类号：
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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