DISTRIBUTION OF COMPLEX ALGEBRAIC NUMBERS

被引：2

作者：

Goetze, Friedrich ^{[1
]}

Kaliada, Dzianis ^{[2
]}

Zaporozhets, Dmitry ^{[3
]}

机构：

[1] Univ Bielefeld, Dept Math, POB 10 01 31, D-33501 Bielefeld, Germany

[2] Natl Acad Sci Belarus, Inst Math, Surganova Str 11, Minsk 220072, BELARUS

[3] Steklov Inst Math, St Petersburg Dept, Fontanka 27, St Petersburg 191011, Russia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 01期

关键词：

Algebraic numbers; distribution of algebraic numbers; integral polynomials; ROOT SEPARATION; DISTANCE;

D O I：

10.1090/proc/13208

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a region Omega subset of C denote by Psi(Q; Omega) the number of complex algebraic numbers in Omega of degree <= n and naive height <= Q. We show that Psi(Q; Omega) = Q(n+1)/2 zeta(n+1) integral(Omega) psi(z) nu(dz) + O (Q(n)), Q -> infinity, where nu is the Lebesgue measure on the complex plane and the function. will be given explicitly.

引用

页码：61 / 71

页数：11

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