On the error-sum function of pierce expansions

DOI10.4171/jfg/142zbMath1527.28003arXiv2302.14280OpenAlexW4387010637MaRDI QIDQ6080846

Min Woong Ahn

Publication date: 25 October 2023

Published in: Journal of Fractal Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.14280

zbMATH Keywords

covering dimensionHausdorff dimensionbox-counting dimensionerror-sum functionpierce expansion

Mathematics Subject Classification ID

Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Other functions defined by series and integrals (33E20) Fractals (28A80) Iteration of real functions in one variable (26A18) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Cites Work

• On the error-sum function of tent map base series
• On the error-sum function of Lüroth series
• Representations of real numbers by infinite series
• On the radius of convergence of \(q\)-series
• A study of topological conjugacies between alternate representation systems
• Large and moderate deviation principles for alternating Engel expansions
• Topological dimension and dynamical systems. Translated from the French by the author
• The continued fraction expansion of certain Pierce series
• Variations on an error sum function for the convergents of some powers of $e$
• Hausdorff dimension of the graph of the error-sum function of $\alpha$-Lüroth series
• New bounds on the length of finite pierce and Engel series
• On the fractional dimension of sets of continued fractions
• On a problem of Alfréd Rényi
• On the error-sum function of alternating Lüroth series
• Ergodic Theory
• The error-sum function of continued fractions
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