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

Authors

HAIBO CHEN
WENBO WANG
MIN YU

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.

DOI

10.3906/mat-1309-63

Keywords

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

First Page

803

Last Page

811

Recommended Citation

CHEN, H, WANG, W, & YU, M (2014). Hausdorff dimension of the graph of the error-sum function of \alpha-Lüroth series. Turkish Journal of Mathematics 38 (5): 803-811. https://doi.org/10.3906/mat-1309-63