On arithmetical nature of Tichy-Uitz's function

Abstract

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