Modular Counting of Rational Points over Finite Fields
نویسندگان
چکیده
منابع مشابه
Modular Counting of Rational Points over Finite Fields
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 non-zero 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)(h+b)p) bit operations. This is singly exponential in each of the parameters {h, b, p}, ...
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We consider the problem of counting the number of points on a plane curve, given by a homogeneous polynomial F E Fp[x, y, 21, which is rational over the ground field IFp. More precisely, we show that if we are given a projective plane curve C of degree n, and if C has only ordinary multiple points, then one can compute the number of IFp-rational points on C in randomized time (logp)" where A = ...
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متن کاملRational Points on Curves over Finite Fields
Preface These notes treat the problem of counting the number of rational points on a curve defined over a finite field. The notes are an extended version of an earlier set of notes Aritmetisk Algebraisk Geometri – Kurver by Johan P. Hansen [Han] on the same subject. In Chapter 1 we summarize the basic notions of algebraic geometry, especially rational points and the Riemann-Roch theorem. For th...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2007
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-007-0245-y