Uniform Distribution of Prime Powers and sets of Recurrence and van der Corput sets in Z^k

Grigori Kolesnik; Manfred Madritsch; Robert Tichy; Vitaly Bergelson; Younghwan Son

arxiv: 1304.4641 · v4 · pith:B5KDUDTFnew · submitted 2013-04-16 · 🧮 math.DS

Uniform Distribution of Prime Powers and sets of Recurrence and van der Corput sets in Z^k

Vitaly Bergelson , Grigori Kolesnik , Manfred Madritsch , Younghwan Son , Robert Tichy This is my paper

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keywords setscorputpowersprimerecurrenceresultsbergelsondistribution

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We establish new results on sets of recurrence and van der Corput sets in Z^k which refine and unify some of the previous results obtained by Sarkozy, Furstenberg, Kamae and Mendes France, and Bergelson and Lesigne. The proofs utilize a general equidistribution result involving prime powers which is of independent interest.

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Uniform Distribution of Prime Powers and sets of Recurrence and van der Corput sets in Z^k

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