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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| Published in | Journal of the Australian Mathematical Society (2001) Vol. 89; no. 2; pp. 233 - 244 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.10.2010
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1446-7887 1446-8107 1446-8107 |
| DOI | 10.1017/S1446788710001503 |
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| Abstract | 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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| AbstractList | 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. |
| Author | KANEKO, HAJIME |
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| References | S1446788710001503_ref11 S1446788710001503_ref10 S1446788710001503_ref16 Dajani (S1446788710001503_ref8) 2006; 15 S1446788710001503_ref15 S1446788710001503_ref14 S1446788710001503_ref13 S1446788710001503_ref17 S1446788710001503_ref1 Borel (S1446788710001503_ref4) 1950; 230 S1446788710001503_ref7 Locher (S1446788710001503_ref12) 1999; 89 Evertse (S1446788710001503_ref9) 2002; 548 S1446788710001503_ref2 S1446788710001503_ref3 S1446788710001503_ref5 Bugeaud (S1446788710001503_ref6) 2007; 118 |
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| Snippet | 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... |
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| SubjectTerms | 11K60 Algebra algebraic numbers Binary digits binary expansions Lower bounds nonadjacent form primary 11K16 secondary 11J71 |
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| Title | ON THE BINARY DIGITS OF ALGEBRAIC NUMBERS |
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