Hausdorff dimension of the graph of the error-sum function of α-L¨uroth series

Abstract

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