Glasner sets and polynomials in primes期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Glasner sets and polynomials in primes

Authors:	R Nair S L Velani

Institution:	Department of Pure Mathematics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, United Kingdom ; Department of Mathematics, Imperial College, University of London, Huxley Building, 180 Queen's Gate, London SW7 2BZ, United Kingdom

Abstract:	A set of integers is said to be Glasner if for every infinite subset of the torus $\mathbb{T}=\mathbb{R}/\mathbb{Z}$ and $\varepsilon>0$ there exists some $n\in S$ such that the dilation $nA=\{nx\colon x\in A\}$ intersects every integral of length $\varepsilon$ in $\mathbb{T}$ . 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 $(f(p_n))_{n\geq 1}$ is Glasner. The theorem is proved in a quantitative form and generalizes a result of Alon and Peres (1992).

Keywords:

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文