On arithmetical nature of Tichy-Uitz's function

TL;DR

This paper investigates the arithmetical properties of a specific singular function from a family introduced by Tichy and Uitz, focusing on the case where the parameter is related to the golden ratio.

Contribution

It provides a detailed analysis of the arithmetical nature of the Tichy-Uitz function for a particular parameter value, extending understanding of its properties.

Findings

Identifies the arithmetical characteristics of g_λ for λ=(3−√5)/2

Connects the function's properties to number theory and algebraic structures

Enhances understanding of singular functions related to continued fractions

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 $\lambda = \frac{3-\sqrt{5}}{2}$.