Some reductions on Jacobian problem in two variables
نویسندگان
چکیده
منابع مشابه
Some Reductions on Jacobian Problem in Two Variables
Let f = (f1, f2) be a regular sequence of affine curves in C. Under some reduction conditions achieved by composing with some polynomial automorphisms of C, we show that the intersection number of curves (fi) in C 2 equals to the coefficient of the leading term x in g2, where n = deg fi (i = 1, 2) and (g1, g2) is the unique solution of the equation yJ(f) = g1f1 + g2f2 with deg gi ≤ n−1. So the ...
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Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
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We prove that all polynomials in several variables can be decomposed as the sums of kth powers: P (x1, . . . , xn) = Q1(x1, . . . , xn) + · · ·+Qs(x1, . . . , xn), provided that elements of the base field are themselves sums of kth powers. We also give bounds for the number of terms s and the degree of the Qi . We then improve these bounds in the case of two variables polynomials of large degre...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2004
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2003.09.001