On the error-sum function of Lüroth series

Abstract

We introduce the error-sum function of Lüroth series. Some elementary properties of this function are studied. We also determine the Hausdorff dimension of the graph of this function.

Convergence Results forr-Iterated Means of the Denominators of the Lüroth Series

“…where Lüroth series have been investigated, for instance, in [1], [3], [4], [5], [11], [12], [13], [14], [15]. The papers [6], [7] consider a variant of Lüroth series, the socalled alternating Lüroth series .…”

The efficiency of approximating real numbers by Lüroth expansion

“…The spectrum analysis of the frequency of the digits of {d n } n 1 was given in [1], [6]. The growth speed of the sequence {d n (x)} n 1 was studied in [14].…”

The fractional dimensional theory in Lüroth expansion

“…For dynamical properties, the transformation T is invariant and ergodic with respect to the Lebesgue measure ( [2], ( [7], p. 80), [9], [13]). And for more research related to Lüroth expansions, we can refer to [3], [7], [12] and [14]. For the exceptional sets in Lüroth expansions, the earliest research was conducted by Šalát in [12], where the author obtained the Hausdorff dimension of the sets…”