On sums and products of integers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

On sums and products of integers

Authors:	Melvyn B Nathanson

Institution:	Department of Mathematics, Lehman College (CUNY), Bronx, New York 10468

Abstract:	Erdos and Szemerédi conjectured that if is a set of positive integers, then there must be at least $k^{2-\varepsilon }$ integers that can be written as the sum or product of two elements of . Erdos and Szemerédi proved that this number must be at least $c k^{1 + \delta }$ for some $\delta > 0$ and $k \geq k_0$ . In this paper it is proved that the result holds for $\delta = 1/31$ .

Keywords:	Additive number theory sumsets sums and products of integers

	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