报 告 题 目：On sets containing no geometric progression

主 讲 人：方 金 辉

单 位：南京信息工程大学

时 间：6月29日14:00

腾 讯 ID：239-996-019

密 码：123456

摘 要：

For k≥3 , we call a set G⊆(0,1] of real numbers k-good if G contains no geometric progression of length k with integer ratio r>1. A real number x∈(0,1]\G is called k-bad with respect to G if G∪{x} contains the k-term progression (x,xr,xr²,...xr^k-1) for some integer r > 1. Defifine Bad(G)={x∈(0,1]\G:x is k-bad with respect to G}. In 2015, Nathanson and O’Bryant showed there exists a unique sequence of integers {1=A₁^(k)<A₂^(k)<…}such that G^(k)=∪^∞_i=1 (1/A_2i^(k),1/A_2i-1^(k)]is a k-good set and Bad(G^(k))=∪^∞_i=1 (1/A_2i+1^(k),1/A_2i^(k)]. The values of A_i^(k) for 2≤i≤4 have previously been found by Nathanson and O’Bryant. We further obtain the value of A₅^(k) and f A₆^(k) .This is a joint work with Xue-Qin Cao and Nathan McNew.

简 介：

方金辉，南京信息工程大学教授、博士生导师。主要研究加法补集、子集和等数论问题，先后主持国家自然科学基金青年项目，面上项目，在Acta Arith., J. Number Theory, J. Combin. Theory Ser. A, Combinatorica等杂志上发表论文50余篇。