Beta-expansions of rational numbers in quadratic Pisot bases

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>

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

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

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)

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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