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.

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

Full Text: PDF