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Roman Urban
Sequences of algebraic integers and density modulo $1$
Journal de théorie des nombres de Bordeaux, 19 no. 3 (2007), p. 755-762, doi: 10.5802/jtnb.610
Article PDF | Reviews Zbl 1157.11030
Keywords: Density modulo $1,$ algebraic integers, topological dynamics, ID-semigroups

Résumé - Abstract

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

\begin{equation*} \lbrace \mu ^m\lambda ^n\xi +r_m:n,m\in \mathbb{N}\rbrace , \end{equation*}

where $\lambda ,\mu \in \mathbb{R}$ is a pair of rationally independent algebraic integers of degree $d\ge 2,$ satisfying some additional assumptions, $\xi \ne 0,$ and $r_m$ is any sequence of real numbers.

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