# On the topology of polynomials with bounded integer coefficients

Journal of the European Mathematical Society (2016)

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

## Access Full Article

top## Abstract

top## How to cite

topFeng, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.