Asymptotic distribution and symmetric means of algebraic numbers

Igor E. Pritsker. "Asymptotic distribution and symmetric means of algebraic numbers." Acta Arithmetica 168.2 (2015): 121-138. <http://eudml.org/doc/278944>.

@article{IgorE2015,
abstract = {Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the problem that include questions on the smallest limit points of symmetric means. The key tool used in the study is the asymptotic distribution of algebraic numbers understood via the weak* limits of their counting measures. We establish interesting properties of the limiting measures, and find the smallest limit points of symmetric means for totally positive algebraic numbers of small height.},
author = {Igor E. Pritsker},
journal = {Acta Arithmetica},
keywords = {polynomials; distribution of zeros; symmetric means; limit points; algebraic numbers},
language = {eng},
number = {2},
pages = {121-138},
title = {Asymptotic distribution and symmetric means of algebraic numbers},
url = {http://eudml.org/doc/278944},
volume = {168},
year = {2015},
}

TY - JOUR
AU - Igor E. Pritsker
TI - Asymptotic distribution and symmetric means of algebraic numbers
JO - Acta Arithmetica
PY - 2015
VL - 168
IS - 2
SP - 121
EP - 138
AB - Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the problem that include questions on the smallest limit points of symmetric means. The key tool used in the study is the asymptotic distribution of algebraic numbers understood via the weak* limits of their counting measures. We establish interesting properties of the limiting measures, and find the smallest limit points of symmetric means for totally positive algebraic numbers of small height.
LA - eng
KW - polynomials; distribution of zeros; symmetric means; limit points; algebraic numbers
UR - http://eudml.org/doc/278944
ER -