A recurrence property of smooth functions

Daniel Berend

doi:10.1007/BF02767351

A recurrence property of smooth functions

Daniel Berend

Research output: Contribution to journal › Article › peer-review

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Abstract

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 de³ log 14 e³, 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 language	English
Pages (from-to)	32-36
Number of pages	5
Journal	Israel Journal of Mathematics
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/BF02767351
State	Published - 1 Feb 1988

ASJC Scopus subject areas

General Mathematics

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title = "A recurrence property of smooth functions",

abstract = "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].",

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N2 - 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].

AB - 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].

UR - https://www.scopus.com/pages/publications/51249177664

U2 - 10.1007/BF02767351

DO - 10.1007/BF02767351

M3 - Article

AN - SCOPUS:51249177664

SN - 0021-2172

VL - 62

SP - 32

EP - 36

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

A recurrence property of smooth functions

Abstract

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