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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

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Equidistribution of $(2^nx)$, $x$ irrational

I've run into a scenario where it would be extremely useful to know if, for $x$ irrational, the sequence $\{(2^nx)\}$ is equidistributed on in $[0,1]$, where $(\cdot)$ denotes the ``fractional part" o …