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THE RELATIVE CONVERGENCE SPEED FOR ENGEL EXPANSIONS AND HAUSDORFF DIMENSION

ZHENLIANG ZHANG

https://orcid.org/0000-0002-5874-2088

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, P. R. China

E-mail Address: zhliang_zhang@163.com

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and

XIAOYAN TAN

School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, P. R. China

E-mail Address: miniyan_tan@163.com

Corresponding author.

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https://doi.org/10.1142/S0218348X21501061Cited by:0 (Source: Crossref)

Abstract

In this paper, we investigate how many real numbers can be well approximated by their convergents in the Engel expansions. Furthermore, the relative growth rate of convergence speed of convergents in the Engel expansion of an irrational number is studied to the rate of growth of its digits. The Hausdorff dimension of exceptional sets of points with a given relative growth rate is established.

Keywords:

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