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On normal numbers mod $2$

Youngho Ahn; Geon Choe — 1998

Colloquium Mathematicae

It is proved that a real-valued function $f (x) = exp (π i χ_{I} (x))$ , where I is an interval contained in [0,1), is not of the form $f (x) = \bar{q (2 x)} q (x)$ 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.

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