Affiliation:
1. Oude Larenseweg 26 7214 PC Epse , THE NETHERLANDS
Abstract
Abstract
Denote by Θ1,Θ2, · · · the sequence of approximation coefficients of Minkowski’s diagonal continued fraction expansion of a real irrational number x. For almost all x this is a uniformly distributed sequence in the interval [0, 1/2 ]. The average distance between two consecutive terms of this sequence and their correlation coefficient are explicitly calculated and it is shown why these two values are close to 1/6 and 0, respectively, the corresponding values for a random sequence in [0, 1/2].
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