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ON THE BINARY DIGITS OF ALGEBRAIC NUMBERS

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  13 October 2010

HAJIME KANEKO
HAJIME KANEKO*
Affiliation:
Department of Mathematics, Kyoto University, Oiwake-tyou, Kitashirakawa, Kyoto-shi, Kyoto 606-8502, Japan (email: [email protected])
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Abstract

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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.

Keywords

algebraic numbersbinary expansionsnonadjacent form

MSC classification

Secondary: 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. 11K60: Diophantine approximation
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 2 , October 2010 , pp. 233 - 244
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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