Spatial Equidistribution of Binomial Coefficients Modulo Prime Powers

Guy Barat; Peter J. Grabner

doi:10.1515/udt-2016-0017

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Spatial Equidistribution of Binomial Coefficients Modulo Prime Powers

Uniform distribution theory

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

By: Guy Barat and Peter J. Grabner

Open Access

|Jan 2017

Abstract

The spatial distribution of binomial coefficients in residue classes modulo prime powers is studied. It is proved inter alia that empirical distribution of the points (k,m)p⁻^m with 0 ≤ k ≤ n < p^m and $(\begin{matrix} n \\ k \end{matrix}) \equiv a {(\mod p)}^{s}$ $\left( {\matrix{n \cr k \cr } } \right) \equiv a\left( {\bmod \;p} \right)^s $ (for (a, p) = 1) for m→∞ tends to the Hausdorff measure on the “p-adic Sierpiński gasket”, a fractals studied earlier by von Haeseler, Peitgen, and Skordev.

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Articles in this issue

DOI: https://doi.org/10.1515/udt-2016-0017 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 151 - 161

Submitted on: May 10, 2016

Accepted on: Jun 14, 2016

Published on: Jan 13, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Binomial coefficients,

equidistribution

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2017 Guy Barat, Peter J. Grabner, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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