A sharp result on <IMG BORDER="0" SRC="/proc/2007-135-11/S0002-9939-07-08890-9/gif-title0/img1.gif" >-covers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

A sharp result on -covers

Authors:	Hao Pan Zhi-Wei Sun

Institution:	Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China ; Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China

Abstract:	Let $A=\{a_{s}+n_{s}\mathbb{Z} \}_{s=1}^{k}$ be a finite system of residue classes which forms an -cover of $\mathbb{Z}$ (i.e., every integer belongs to at least members of ). In this paper we show the following sharp result: For any positive integers $m_{1},\ldots ,m_{k}$ and $\theta \in 0,1)$ , if there is $I\se \{1,\ldots ,k\}$ such that the fractional part of $\sum _{s\in I} m_{s}/n_{s}$ is $\theta$ , then there are at least $2^{m}$ such subsets of $\{1,\ldots ,k\}$ . This extends an earlier result of M. Z. Zhang and an extension by Z. W. Sun. Also, we generalize the above result to -covers of the integral ring of any algebraic number field with a power integral basis.

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