Sequences of algebraic integers and density modulo $1$

Urban, Roman

doi:10.5802/jtnb.610

Sequences of algebraic integers and density modulo

1

Urban, Roman ¹

¹ Institute of Mathematics Wroclaw University Plac Grunwaldzki 2/4 50-384 Wroclaw, Poland

Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 3, pp. 755-762.

Résumé
Abstract

Nous établissons la densité modulo $1$ des ensembles de la forme

{μ^{m} λ^{n} ξ + r_{m} : n, m \in ℕ},

où $λ, μ \in ℝ$ sont deux entiers algébriques de degré $d \geq 2,$ qui sont rationnellement indépendants et satisfont des hypothèses techniques supplémentaires, $ξ \neq 0,$ et $r_{m}$ une suite quelconque de nombres réels.

We prove density modulo $1$ of the sets of the form

{μ^{m} λ^{n} ξ + r_{m} : n, m \in ℕ},

where $λ, μ \in ℝ$ is a pair of rationally independent algebraic integers of degree $d \geq 2,$ satisfying some additional assumptions, $ξ \neq 0,$ and $r_{m}$ is any sequence of real numbers.

Zbl

DOI : 10.5802/jtnb.610

Mots clés : Density modulo $1,$ algebraic integers, topological dynamics, ID-semigroups

Affiliations des auteurs :

Urban, Roman ¹

¹ Institute of Mathematics Wroclaw University Plac Grunwaldzki 2/4 50-384 Wroclaw, Poland

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     title = {Sequences of algebraic integers and density modulo~$1$},
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     publisher = {Universit\'e Bordeaux 1},
     volume = {19},
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     year = {2007},
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     url = {http://www.numdam.org/articles/10.5802/jtnb.610/}
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Urban, Roman. Sequences of algebraic integers and density modulo $1$. Journal de théorie des nombres de Bordeaux, Tome 19 (2007) no. 3, pp. 755-762. doi : 10.5802/jtnb.610. http://www.numdam.org/articles/10.5802/jtnb.610/

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