Weyl’s Uniform Distribution Under Periodic Perturbation

Totik, Vilmos

doi:10.2478/udt-2022-0015

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Weyl’s Uniform Distribution Under Periodic Perturbation

Uniform distribution theory

Volume 17 (2022): Issue 2 (December 2022)

By: Vilmos Totik

Open Access

|Dec 2022

Abstract

We examine the uniform distribution theory of H. Weyl when there is a periodic perturbation present. As opposed to the classical setting, in this case the conditions for (mod 1) density and (mod 1) uniform distribution turn out to be different.

References

[1] BOHR, H.: Almost Periodic Functions. Publishing Co., New York, N. Y., 1947. (Translation from German; originally published Berlin 1933.)
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[2] HARDY, G. H.—WRIGHT, E. M.: An Introduction to the Theory of Numbers.Sixth edition. (Revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles.) Oxford University Press, Oxford, 2008.10.1093/oso/9780199219858.002.0002
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[3] KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences. Pure and App. Math. Wiley-Interscience [John Wiley & Sons], New York, 1974.
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[4] RUDIN, W.: Real and Complex Analysis. 3rd edition. McGraw-Hill Book Co., New York, 1987.
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[5] WEYL, H.:Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77 (1916), no. 3, 313–352.10.1007/BF01475864
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DOI: https://doi.org/10.2478/udt-2022-0015 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 127 - 160

Submitted on: May 6, 2022

Accepted on: Aug 28, 2022

Published on: Dec 12, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Weyl’s theory,

density (mod 1),

uniform distribution (mod 1),

polynomial sequences,

vector sequences,

periodic perturbations

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2022 Vilmos Totik, 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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