Finiteness in real cubic fields
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F17%3A00311996" target="_blank" >RIV/68407700:21340/17:00311996 - 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
Finiteness in real cubic fields
Original language description
We study finiteness property in numeration systems with cubic Pisot unit base. A base $beta>1$ is said to satisfy property (F), if the set ${rm Fin}(beta)$ of numbers with finite $beta$-expansions forms a ring. We show that in every real cubic field which is not totally real, there exists a cubic Pisot unit satisfying (F). On the other hand, there exist totally real cubic fields without such a unit. In such fields, however, one finds a cubic Pisot unit $beta>1$ satisfying property ($-$F), i.e., the set ${rm Fin}(-beta)$ of finite $(-beta)$-expansions forms a ring.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA13-03538S" target="_blank" >GA13-03538S: Algorithms, Dynamics and Geometry of Numeration systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Acta Mathematica Hungarica
ISSN
0236-5294
e-ISSN
1588-2632
Volume of the periodical
153
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
16
Pages from-to
318-333
UT code for WoS article
000414778000004
EID of the result in the Scopus database
2-s2.0-85029487524