On normal numbers mod $2$

Volume 76 / 1998

Youngho Ahn, Geon Choe Colloquium Mathematicum 76 (1998), 161-170 DOI: 10.4064/cm-76-2-161-170


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.


  • Youngho Ahn
  • Geon Choe

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