Equidistributions of Sign Patterns of the Liouville Function and Normal Numbers

preprint2023arXivOpen access

The equidistribution of the double sign patterns of the Liouville function $λ$ is proved unconditionally. As application, it is shown that the computable real number $\sum_{n \geq 1} \frac{1+λ(n)}{2^{n}}$ is a simply normal number in base 4.

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Equidistributions of Sign Patterns of the Liouville Function and Normal Numbers

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