Sur Les Parties Fractionnaires Des Suites (βn)n≥1

Anne Bertrand-Mathis

doi:10.2478/udt-2019-0014

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Sur Les Parties Fractionnaires Des Suites (βn)n≥1

Uniform distribution theory

Volume 14 (2019): Issue 2 (December 2019)

By: Anne Bertrand-Mathis

Open Access

|Mar 2020

Abstract

We show that for an arbitrary sequence of intervals I_n with constant length c, there exist real numbers β such that for all n βⁿ belongs to I_n modulo one.

References

[1] KAHANE, J. P.—SALEM, R.: Ensembles Parfaits et Séries Trigonométriques.In: Actualités Sci. Indust. Vol. 1301, Hermann, Paris, 1963.
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[2] KOKSMA, J. F.: Ein mengentheoretischer Satz über die Gleichverteilung modulo Eins, Compositio Mathematica, 2 (1935), 250–258.
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Articles in this issue

DOI: https://doi.org/10.2478/udt-2019-0014 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 69 - 72

Submitted on: Jul 19, 2018

Accepted on: Jun 28, 2018

Published on: Mar 27, 2020

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Distribution modulo one,

sequence of intervals,

exponential sequence

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2020 Anne Bertrand-Mathis, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 14 (2019): Issue 2 (December 2019)