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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.
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Is $\lfloor \log(n!)\rfloor \alpha$ equidistributed on the unit circle?
In this question $\lfloor a\rfloor$ means the greatest integer not exceeding $a$.
Using van der Corput's inequalities one is able to show that $\log(n!)\alpha$ is equidistributed on the unit circle …