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Journals / Turkish Journal of Mathematics / 2014 / Cilt: 38 - Sayı: 5

Hausdorff dimension of the graph of the error-sum function of a-Lüroth series

Haibo CHEN
Wenbo WANG
Min YU
Pages
803–811
Publication Date
2014-05-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some other properties of the error-sum function are also investigated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let a be a countable partition of the unit interval [0,1].
📊
Key Findings & Data:In this paper, we will introduce the error-sum function of a-Lüroth series and determine the Hausdorff dimension of its graph when the partition a is eventually decreasing.
💡
Conclusion & Impact:Some other properties of the error-sum function are also investigated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Hausdorff dimension · the a-Lüroth series · error-sum function

Abstract

Let a be a countable partition of the unit interval [0,1]. In this paper, we will introduce the error-sum function of a-Lüroth series and determine the Hausdorff dimension of its graph when the partition a is eventually decreasing. Some other properties of the error-sum function are also investigated.

Özet

Let a be a countable partition of the unit interval [0,1]. In this paper, we will introduce the error-sum function of a-Lüroth series and determine the Hausdorff dimension of its graph when the partition a is eventually decreasing. Some other properties of the error-sum function are also investigated.

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Cite This Article

CHEN, H., WANG, W., YU, M. (2014). Hausdorff dimension of the graph of the error-sum function of a-Lüroth series. Turkish Journal of Mathematics, Cilt: 38 - Sayı: 5, 803–811. https://ajindex.com/articles/723315

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References (7)

  1. Chen HB, Wen ZX. The Hausdorff dimension of certain sets in a class of α -L¨uroth expansions. Sci China Math 2014; 52: 303–313.
  2. Dai MF, Tang LX. On the error-sum function of tent map base series. J Math Anal Appl 2011; 378: 571–577.
  3. Elsner C, Stein M. On error sum functions formed by convergents of real numbers. J Integer Sequences 2011; 14: 11.8.6. Falconer K. Fractal Geometry: Mathematical Foundations and Applications. West Sussex, UK: John Wiley & Sons, 1990.
  4. Grigorescu S, Iosifescu M. Dependence with Complete Connections and Its Applications. Cambridge, UK: Cam- bridge University Press, 1990.
  5. Kalpazidou S, Knopfmacher A, Knopfmacher J. Metric properties of alternating L¨uroth series. Portugaliae Mathe- matica 1991; 48: 319–325. Kesseb¨ohmer K, Munday S, Stratmann BO. Strong renewal theorems and Lyapunov spectra for α -Farey and α -L¨uroth systems. Ergod Theor Dyn Syst 2012; 32: 989–1017. Munday S. A note on Diophantine-type fractals for α -L¨uroth systems. Intergers 2011; 11: 1–14.
  6. Ridley JN, Petruska G. The error-sum function of continued fractions. Indagat Math 2000; 11: 273–282.
  7. Shen LM, Wu J. On the error-sum function of L¨uroth series. J Math Anal Appl 2007; 329: 1440–1445.