A Note on the Continued Fraction of Minkowski

Jager, Hendrik

doi:10.1515/udt-2017-0019

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A Note on the Continued Fraction of Minkowski

Uniform distribution theory

Volume 12 (2017): Issue 2 (December 2017)

By: Hendrik Jager

Open Access

|Jan 2018

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].

References

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DOI: https://doi.org/10.1515/udt-2017-0019 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 125 - 130

Submitted on: Oct 10, 2016

Accepted on: Feb 15, 2017

Published on: Jan 30, 2018

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

11K50

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2018 Hendrik Jager, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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