Beta-expansions of rational numbers in quadratic Pisot bases
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F18%3A00305590" target="_blank" >RIV/68407700:21340/18:00305590 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/18:10383191
Result on the web
<a href="https://doi.org/10.4064/aa8260-11-2017" target="_blank" >https://doi.org/10.4064/aa8260-11-2017</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/aa8260-11-2017" target="_blank" >10.4064/aa8260-11-2017</a>
Alternative languages
Result language
angličtina
Original language name
Beta-expansions of rational numbers in quadratic Pisot bases
Original language description
We study rational numbers with purely periodic Rényi β-expansions. For bases β satisfying β2=aβ+b with b dividing a, we give a necessary and sufficient condition for all rational numbers p/qelement[0,1) with gcd(q,b)=1 to have a purely periodic β-expansion. We provide a simple algorithm for determining the infimum of p/qelement[0,1) with gcd(q,b)=1 and whose β-expansion is not purely periodic, which works for all quadratic Pisot numbers β.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Acta Arithmetica
ISSN
0065-1036
e-ISSN
1730-6264
Volume of the periodical
183
Issue of the periodical within the volume
1
Country of publishing house
PL - POLAND
Number of pages
17
Pages from-to
35-51
UT code for WoS article
000427918800002
EID of the result in the Scopus database
2-s2.0-85044079137