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Convergence Results for r-Iterated Means of the Denominators of the Lüroth Series

Jan 13, 2017

Convergence Results for r-Iterated Means of the Denominators of the Lüroth Series's Cover Image

Uniform distribution theory

Volume 11 (2016): Issue 2 (December 2016)

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Published Online: Jan 13, 2017

Page range: 179 - 203

Received: Mar 30, 2016

Accepted: Oct 17, 2016

DOI: https://doi.org/10.1515/udt-2016-0020

Keywords
Lüroth series, convergence in probability, convergence in distribution, iterated arithmetic means, iterated weighted means

© 2016 Rita Giuliano, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the Lüroth series and obtain new theorems concerning the same two kinds of convergence for the r-iterated arithmetic means of such denominators. These results are extended to r-iterated weighted means.

Language:: English

Publication timeframe:: 2 times per year
Journal Subjects:: Mathematics, Algebra and Number Theory, Discrete Mathematics, Probability and Statistics, Numerical and Computational Mathematics

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