Geodesic
Asymptotic distribution and symmetric means of algebraic numbers
Igor E. Pritsker1
1 Department of Mathematics Oklahoma State University Stillwater, OK 74078, U.S.A.
Acta Arithmetica, Tome 168 (2015) no. 2, pp. 121-138 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa168-2-3
Keywords: schur introduced problem smallest limit point arithmetic means totally positive conjugate algebraic integers area developed further siegel smyth others consider several generalizations problem include questions smallest limit points symmetric means key tool study asymptotic distribution algebraic numbers understood via weak * limits their counting measures establish interesting properties limiting measures smallest limit points symmetric means totally positive algebraic numbers small height

Igor E. Pritsker 1

1 Department of Mathematics Oklahoma State University Stillwater, OK 74078, U.S.A. 
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Igor E. Pritsker. Asymptotic distribution and symmetric means
 of algebraic numbers. Acta Arithmetica, Tome 168 (2015) no. 2, pp. 121-138. doi: 10.4064/aa168-2-3

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