NOTE ON THE HAUSDORFF GEOMETRY OF POLYNOMIALS

被引：0

作者：

Sendov, Blagovest

机构：

来源：

COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES | 2010年 / 63卷 / 12期

关键词：

zeroes; critical points and critical values of polynomials; mean value conjecture of Smale; ZEROS;

D O I：

暂无

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Let p(z) = (z - z(1))(z - z(2)) ... (z - z(n)) be a polynomial of degree n >= 2 with distinct zeroes. In this paper is proved that the distance from every zero z(1) of p(z) to the closest critical point of p(z) is not bigger than the distance of z(1) to any other zero of p(z) divided by 2 sin pi/n.

引用

页码：1707 / 1714

页数：8

共 50 条

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