On normal numbers mod $2$
Volume 76 / 1998
Colloquium Mathematicum 76 (1998), 161-170
DOI: 10.4064/cm-76-2-161-170
Abstract
It is proved that a real-valued function $f(x)=\exp(\pi i \chi_I(x))$, where I is an interval contained in [0,1), is not of the form $f(x)=\overline{q(2x)}q(x)$ with |q(x)|=1 a.e. if I has dyadic endpoints. A relation of this result to the uniform distribution mod 2 is also shown.
