## Equidistribution

Prove that if is a sequence of real numbers such that the fractional parts of are equidistributed in for every positive integer , then the fractional parts of are also equidistributed in .

Use this to prove that if is a non-constant polynomial with real coefficients, with at least one of these coefficients irrational, then the fractional parts of are equidistributed in .

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Categories: Analysis, Fourier Analysis
equidistribution, weyl

I have a good idea the solution iis Van der Corput’s difference theorem; see this Terence Tao write-up http://terrytao.wordpress.com/2008/06/14/the-van-der-corputs-trick-and-equidistribution-on-nilmanifolds/

Thank you for the link.