A Note on the Continued Fraction of Minkowski
Hendrik Jager · Uniform distribution theory · 2017
Abstract Denote by Θ 1 ,Θ 2 , · · · 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].