Fractal Subseries of the Harmonic Series

2009/03/12 by Gábor Korvin, Gabor Korvin, Korvin, Gabor
Mathematics · Physics and Astronomy · #11K36 #Advanced Mathematical Theories and Applications #Chaos control and synchronization #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11K36

paper · pdf · doi:10.48550/arxiv.0903.2141

No part was published or presented before

arxiv created 2009/03/12 · openalex publication_date 2009/03/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the frequency distribution of some of the digits does not exist. Examples are given for irregular sequences where the corresponding harmonic subseries is convergent, or divergent, respectively.

Citations

• Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
• Fractal Geometry: Mathematical Foundations and Applications.
• Distribution of frequencies of digits via multifractal analysis

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