A recurrence property of smooth functions

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4 Scopus citations


Let P and Q be real polynomials of degrees d and e, respectively, and f a periodic function. It is shown that, if f is s times differentiable at Q(0), where s≧7 de 3 log 14 e 3, then for every e{open}>0 the diophantine inequality ≧FF5C;P(x)f(Q(x)) -P(0)f(Q(0)) -y≧ εx≠0, has a solution. This settles in particular a question raised by Furstenberg and Weiss [6].

Original languageEnglish
Pages (from-to)32-36
Number of pages5
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Feb 1988

ASJC Scopus subject areas

  • General Mathematics


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