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- Title
A note on approximation efficiency and partial quotients of Engel continued fractions.
- Authors
Hu, Hui; Yu, Yueli; Zhao, Yanfen
- Abstract
We consider the efficiency of approximating real numbers by their convergents of Engel continued fractions (ECF). Specifically, we estimate the Hausdorff dimension of the set of points whose ECF-convergents are the best approximations infinitely often. We also obtain the Hausdorff dimensions of the Jarnik-like set and the related sets defined by some growth rates of partial quotients in ECF expansions.
- Subjects
REAL numbers; ENGEL'S law; ECONOMIC convergence; APPROXIMATION theory; FRACTAL dimensions
- Publication
International Journal of Number Theory, 2017, Vol 13, Issue 9, p2433
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042117501329