# On the limit points of the fractional parts of powers of Pisot numbers

Archivum Mathematicum (2006)

- Volume: 042, Issue: 2, page 151-158
- ISSN: 0044-8753

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topDubickas, Artūras. "On the limit points of the fractional parts of powers of Pisot numbers." Archivum Mathematicum 042.2 (2006): 151-158. <http://eudml.org/doc/249821>.

@article{Dubickas2006,

abstract = {We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots $, where $\alpha >1$ is a Pisot number and $\xi \in \{\mathbb \{Q\}\}(\alpha )$ is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where $\xi =1$ and the unique limit point is zero, was earlier described by the author and Luca, independently.},

author = {Dubickas, Artūras},

journal = {Archivum Mathematicum},

keywords = {Pisot numbers; fractional parts; limit points; Pisot numbers; fractional parts; limit points},

language = {eng},

number = {2},

pages = {151-158},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On the limit points of the fractional parts of powers of Pisot numbers},

url = {http://eudml.org/doc/249821},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Dubickas, Artūras

TI - On the limit points of the fractional parts of powers of Pisot numbers

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 2

SP - 151

EP - 158

AB - We consider the sequence of fractional parts $\lbrace \xi \alpha ^n\rbrace $, $n=1,2,3,\dots $, where $\alpha >1$ is a Pisot number and $\xi \in {\mathbb {Q}}(\alpha )$ is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where $\xi =1$ and the unique limit point is zero, was earlier described by the author and Luca, independently.

LA - eng

KW - Pisot numbers; fractional parts; limit points; Pisot numbers; fractional parts; limit points

UR - http://eudml.org/doc/249821

ER -

## References

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