| 某些Ruzsa数$R_m$的新上界 |
| |
| 引用本文： | 汤敏,陈永高.某些Ruzsa数$R_m$的新上界[J].数学研究及应用,2010,30(3):557-561. |
| |
| 作者姓名： | 汤敏 陈永高 |
| |
| 作者单位： | 安徽师范大学数学系, 安徽 芜湖 241000;南京师范大学数学系, 江苏 南京 210097 |
| |
| 基金项目： | 国家自然科学基金(Grant Nos.10901002; 10771103). |
| |
| 摘 要： | For A ■ Z m and n ∈ Z m ,let σ A (n) be the number of solutions of equation n = x + y,x,y ∈ A.Given a positive integer m,let R m be the least positive integer r such that there exists a set A ■ Z m with A + A = Z m and σ A (n) ≤ r.Recently,Chen Yonggao proved that all R m ≤ 288.In this paper,we obtain new upper bounds of some special type R kp 2 .
|
| 关 键 词： | Erdos-Turan conjecture additive bases Ruzsa numbers. |
| 收稿时间： | 2008/11/5 0:00:00 |
| 修稿时间： | 2009/5/16 0:00:00 |
The New Upper Bounds of Some Ruzsa Numbers $R_m$ |
| |
| Min TANG and Yong Gao CHEN.The New Upper Bounds of Some Ruzsa Numbers $R_m$[J].Journal of Mathematical Research with Applications,2010,30(3):557-561. |
| |
| Authors: | Min TANG and Yong Gao CHEN |
| |
| Institution: | 1. Department of Mathematics, Anhui Normal University, Anhui 241000, P. R. China
2. Department of Mathematics, Nanjing Normal University, Jiangsu 210097, P. R. China |
| |
| Abstract: | For $A\subseteq {\mathbf{Z}}_m$ and $n\in {\mathbf{Z}}_m$, let $\sigma_A(n)$ be the number of solutions of equation $n=x+y, x,y\in A$. Given a positive integer $m$, let $R_m$ be the least positive integer $r$ such that there exists a set $A\subseteq {\mathbf{Z}}_m$ with $A+A={\mathbf{Z}}_m$ and $\sigma_A(n)\leq r$. Recently, Chen Yonggao proved that all $R_m\leq 288$. In this paper, we obtain new upper bounds of some special type $R_{kp^2}$. |
| |
| Keywords: | Erd\H{o}s-Tur\'{a}n conjecture additive bases Ruzsa numbers |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |
