On arithmetical nature of Tichy-Uitz's function

Abstract

In [10] R.F. Tichy and J. Uitz introduced a one parameter family $g_{\lambda}$, $\lambda \in (0,1)$ of singular functions. When $\lambda=1/2$ function $g_{\lambda}$ coincides with the famous Minkowski's question mark function. In this paper we describe the arithmetical nature of function $g_{\lambda}$ when $\lambda = \frac{3-\sqrt{5}}{2}$.