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.
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页码：61 / 71
页数：11
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