Normality to Different Bases

Gavin Brown
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Gavin Brown: The University of Adelaide

A chapter in Algorithms, Fractals, and Dynamics, 1995, pp 51-57 from Springer

Abstract: Abstract For a positive integer s(> 1), we say that the real number x is normal to base s or s-normal if the sequence (s n x) n-1 ∞ is uniformly distributed modulo one. Some 80 years ago Borel showed that almost all real numbers are normal to all bases. Some 40 years ago Steinhaus asked whether 2-normality coincides with 3-normality and Cassels answered the question in the negative (see [3]).

Keywords: Haar Measure; Algebraic Number; Diophantine Equation; Base Root; Integer Entry (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4613-0321-3_3

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