# On the topology of polynomials with bounded integer coefficients

• Volume: 018, Issue: 1, page 181-193
• ISSN: 1435-9855

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## Abstract

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For a real number $q>1$ and a positive integer $m$, let ${Y}_{m}\left(q\right):=\left\{{\sum }_{i=0}^{n}{ϵ}_{i}{q}^{i}:{ϵ}_{i}\in \left\{0,±1,...,±m\right\},n=0,1,...\right\}$. In this paper, we show that ${Y}_{m}\left(q\right)$ is dense in $ℝ$ if and only if $q and $q$ is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].

## How to cite

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Feng, De-Jun. "On the topology of polynomials with bounded integer coefficients." Journal of the European Mathematical Society 018.1 (2016): 181-193. <http://eudml.org/doc/277184>.

@article{Feng2016,
abstract = {For a real number $q>1$ and a positive integer $m$, let $Y_m(q):=\left\lbrace \sum ^n_\{i=0\}\epsilon _i q^i : \epsilon _i \in \left\lbrace 0,\pm 1,\ldots , \pm m\right\rbrace , n=0,1,\ldots \right\rbrace$. In this paper, we show that $Y_m(q)$ is dense in $\mathbb \{R\}$ if and only if $q<m+1$ and $q$ is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].},
author = {Feng, De-Jun},
journal = {Journal of the European Mathematical Society},
keywords = {Pisot numbers; iterated function systems; Pisot numbers; iterated function systems},
language = {eng},
number = {1},
pages = {181-193},
publisher = {European Mathematical Society Publishing House},
title = {On the topology of polynomials with bounded integer coefficients},
url = {http://eudml.org/doc/277184},
volume = {018},
year = {2016},
}

TY - JOUR
AU - Feng, De-Jun
TI - On the topology of polynomials with bounded integer coefficients
JO - Journal of the European Mathematical Society
PY - 2016
PB - European Mathematical Society Publishing House
VL - 018
IS - 1
SP - 181
EP - 193
AB - For a real number $q>1$ and a positive integer $m$, let $Y_m(q):=\left\lbrace \sum ^n_{i=0}\epsilon _i q^i : \epsilon _i \in \left\lbrace 0,\pm 1,\ldots , \pm m\right\rbrace , n=0,1,\ldots \right\rbrace$. In this paper, we show that $Y_m(q)$ is dense in $\mathbb {R}$ if and only if $q<m+1$ and $q$ is not a Pisot number. This completes several previous results and answers an open question raised by Erdös, Joó and Komornik [8].
LA - eng
KW - Pisot numbers; iterated function systems; Pisot numbers; iterated function systems
UR - http://eudml.org/doc/277184
ER -

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