Article
A Note on the Continued Fraction of Minkowski
Authors
Abstract
Denote by \( \Theta_1, \Theta_2, \ldots \) 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 \( \left[0, \dfrac{1}{2}\right] \). The average distance between two consecutive terms of this sequence and their correlation coefficient are explicitly calculated and it is shown that these two values are close to \( 1/6 \) and \( 0 \), respectively, the corresponding values for a random sequence in \( \left[0, \dfrac{1}{2}\right] \).
Keywords
Continued fractions, approximation coefficients, metrical theory.
Citation
Jager, H. (2017). A note on the continued fraction of minkowski. Uniform Distribution Theory, 12(2), 125–130. https://doi.org/10.1515/udt-2017-0019
H. Jager, “A note on the continued fraction of minkowski,” Uniform Distribution Theory, vol. 12, no. 2, pp. 125–130, 2017, doi: 10.1515/udt-2017-0019.
Jager H. A note on the continued fraction of minkowski. Uniform Distribution Theory. 2017;12(2):125–130. doi:10.1515/udt-2017-0019.
Jager, H. (2017), ‘A note on the continued fraction of minkowski’, Uniform Distribution Theory, 12(2), pp. 125–130. Available at: https://doi.org/10.1515/udt-2017-0019.
Jager, Hendrik. “A Note on the Continued Fraction of Minkowski.” Uniform Distribution Theory, vol. 12, no. 2, 2017, pp. 125–130. https://doi.org/10.1515/udt-2017-0019.
Jager, Hendrik. “A Note on the Continued Fraction of Minkowski.” Uniform Distribution Theory 12, no. 2 (2017): 125–130. https://doi.org/10.1515/udt-2017-0019.
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Published by: Engineering Journals
