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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%2F00216208%3A11320%2F18%3A10383191" target="_blank" >RIV/00216208:11320/18:10383191 - isvavai.cz</a>

  • Alternative codes found

    RIV/68407700:21340/18:00305590

  • 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 β 2 =aβ+b with b dividing a , we give a necessary and sufficient condition for γ(β)=1 , i.e., that all rational numbers p/qELEMENT OF[0,1) with gcd(q,b)=1 have a purely periodic β -expansion. A simple algorithm for determining the value of γ(β) for all quadratic Pisot numbers β is described.

  • Czech name

  • Czech description

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

    <a href="/en/project/GJ17-04703Y" target="_blank" >GJ17-04703Y: Quadratic forms and numeration systems over number fields</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

  • 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