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%2F14%3A00221915" target="_blank" >RIV/68407700:21340/14:00221915 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Beta-expansions of rational numbers in quadratic Pisot bases
Original language description
We study the purely periodic beta-expansions of rational numbers. We give an algorithm for determining the value of the function gamma(beta) for quadratic Pisot numbers beta. For numbers satisfying beta^2=a beta+b with b dividing a, we show a necessary and sufficient condition for gamma(beta)=1, i.e., that all rational numbers p/q in [0,1) with gcd(q,b)=1 have a purely periodic beta-expansion.
Czech name
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Czech description
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Classification
Type
O - Miscellaneous
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-03538S" target="_blank" >GA13-03538S: Algorithms, Dynamics and Geometry of Numeration systems</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů