Asymptotic distribution and symmetric means of algebraic numbers

• Autorzy: Igor E. Pritsker
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11C08: Polynomials
• 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral)
• 11R09: Polynomials (irreducibility, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 168
• Numer: 2
• Strony: 121-138

Daty

wydano

2015

Twórcy

autor

Igor E. Pritsker

• Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A.

Identyfikatory

DOI

10.4064/aa168-2-3