Aritmetics on beta-expansion

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F04%3A04105339" target="_blank" >RIV/68407700:21340/04:04105339 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Aritmetics on beta-expansion

Original language description

In this paper we consider representation of numbers in an irrational basis $beta>1$. We study the arithmetic operations on $beta$-expansions and provide bounds on the number of fractional digits arising in addition and multiplication, $L_oplus(beta)$and $L_odot(beta)$, respectively. We determine these bounds for irrational numbers $beta$ which are algebraic with at least one conjugate in modulus smaller than 1. In the case of a Pisot number $beta$ we derive the relation between $beta$-integersand cut-and-project sequences and then use the properties of cut-and-project sequences to estimate $L_oplus(beta)$ and $L_odot(beta)$. We generalize the results known for quadratic Pisot units to other quadratic Pisot numbers.

Czech name

Aritmetics on beta-expansion

Czech description

In this paper we consider representation of numbers in an irrational basis $beta>1$. We study the arithmetic operations on $beta$-expansions and provide bounds on the number of fractional digits arising in addition and multiplication, $L_oplus(beta)$and $L_odot(beta)$, respectively. We determine these bounds for irrational numbers $beta$ which are algebraic with at least one conjugate in modulus smaller than 1. In the case of a Pisot number $beta$ we derive the relation between $beta$-integersand cut-and-project sequences and then use the properties of cut-and-project sequences to estimate $L_oplus(beta)$ and $L_odot(beta)$. We generalize the results known for quadratic Pisot units to other quadratic Pisot numbers.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F01%2F0130" target="_blank" >GA201/01/0130: Some aspects of quantum group and self-similar aperiodic structures</a><br>

Continuities

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

Publication year

2004

Confidentiality

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

Name of the periodical

Acta Arith

ISSN

0065-1036

e-ISSN

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Volume of the periodical

112

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

18

Pages from-to

23-40

UT code for WoS article

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EID of the result in the Scopus database

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