Vitaly Bergelson: Generalized polynomials: from Weyl and van der Corput to dynamical systems on nilmanifolds

Generalized polynomials form a natural family of functions which are obtained from the conventional polynomials by the use of the greatest integer function, addition and multiplication. We will review some recent results on Diophantine approximations which extend the classical results of Weyl and van der Corput and discuss the connections between generalized polynomials and dynamical systems.

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