Glasner sets and polynomials in primes
R. Nair and S. L. Velani
Proc. Amer. Math. Soc. 126 (1998), 2835-2840
Primary 11K38; Secondary 11K06, 11J13
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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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Department of Pure Mathematics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, United Kingdom
S. L. Velani
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
William W. Adams
© Copyright 1998
American Mathematical Society