ON THE BINARY DIGITS OF ALGEBRAIC NUMBERS

Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little is known about this problem. We improve the lower bounds for the number of digit changes in the binary expansions of algebraic irrational numbers.

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Bibliographic Details
Published inJournal of the Australian Mathematical Society (2001) Vol. 89; no. 2; pp. 233 - 244
Main Author KANEKO, HAJIME
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.10.2010
Subjects
11K60
Algebra
algebraic numbers
Binary digits
binary expansions
Lower bounds
nonadjacent form
primary 11K16
secondary 11J71
binary expansions
nonadjacent form
primary 11K16; secondary 11J71
11K60
algebraic numbers
Online AccessGet full text
ISSN1446-7887
1446-8107
1446-8107
DOI10.1017/S1446788710001503

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Summary:Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little is known about this problem. We improve the lower bounds for the number of digit changes in the binary expansions of algebraic irrational numbers.
Bibliography:ArticleID:00150
PII:S1446788710001503
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istex:8F4731672E613DE3AEC08896D5B45BEC7486DE96
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1446-7887
1446-8107
1446-8107
DOI:10.1017/S1446788710001503