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,...xrk-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/A2i(k),1/A2i-1(k)]is a k-good set and Bad(G(k))=∪∞i=1 (1/A2i+1(k),1/A2i(k)]. The values of Ai(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。
