Glasner sets and polynomials in primes
Authors: R. Nair and S. L. Velani
Journal: Proc. Amer. Math. Soc. 126 (1998), 2835-2840
MSC (1991): Primary 11K38; Secondary 11K06, 11J13
MathSciNet review: 1452815
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Abstract: A set of integers is said to be Glasner if for every infinite subset of the torus and there exists some such that the dilation intersects every integral of length in . In this paper we show that if denotes the th prime integer and is any non-constant polynomial mapping the natural numbers to themselves, then is Glasner. The theorem is proved in a quantitative form and generalizes a result of Alon and Peres (1992).
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Affiliation: Department of Pure Mathematics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, United Kingdom
S. L. Velani
Affiliation: Department of Mathematics, Imperial College, University of London, Huxley Building, 180 Queen’s Gate, London SW7 2BZ, United Kingdom
Received by editor(s): August 19, 1996
Received by editor(s) in revised form: March 3, 1997
Communicated by: William W. Adams
Article copyright: © Copyright 1998 American Mathematical Society