Hausdorff dimension of the graph of the error-sum function of \alpha-Lüroth series

Authors

HAIBO CHEN
WENBO WANG
MIN YU

DOI

10.3906/mat-1309-63

Abstract

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

Keywords

Hausdorff dimension, the \alpha-Lüroth series, error-sum function

First Page

803

Last Page

811

Recommended Citation

CHEN, HAIBO; WANG, WENBO; and YU, MIN (2014) "Hausdorff dimension of the graph of the error-sum function of \alpha-Lüroth series," Turkish Journal of Mathematics: Vol. 38: No. 5, Article 1. https://doi.org/10.3906/mat-1309-63
Available at: https://journals.tubitak.gov.tr/math/vol38/iss5/1