Statistical properties of the Calkin--Wilf tree: real an p-adic distribution

2007/12/29 by Giedrius Alkauskas, Alkauskas, Giedrius, Jörn Steuding +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories #math.NT #msc:11A55 #msc:26A30

paper · pdf · doi:10.48550/arxiv.0801.0054

19 pages (preprint). Some results of this paper are already well-known, some (p-adic distribution and properties of the moments) are new and will be merged into paper arXiv:0801.0051

arxiv created 2008/09/23 · arxiv updated 2009/12/01

Abstract

We examine statistical properties of the Calkin--Wilf tree and give number-theoretical applications.

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• The moments of Minkowski question mark function: the dyadic period function

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• Calkin-Wilf tree
• Enumerating Trees
• Generalized q-Calkin-Wilf trees and c-hyper m-expansions of integers
• Bounds on tree distribution in number theory
• A brief introduction to p-adic numbers