名称：ON AN ERDÓS SIMILARITY PROBLEM IN THE LARGE

报告专家：YUVESHEN

专家所在单位：英属哥伦比亚大学

报告时间：2023-12-04  上午10点-12点

报告地点: 线上, zoom：894 9350 1808 密码：443038

专家简介：

YUVESHEN ,BC. Vancouver, (UBC), Columbia British of UBC,University at Instructor Class Mathematics,Small in Candidate Ph.D.

报告摘要：

In a recent paper, Kolountzakis and Papageorgiou ask if for every e E (0, 1), there exists a set S∈R such that |S∩I|≥1 - e for every interval I C R with unit length but that does not contain any affine copy of a given increasing sequence of exponential growth or faster. This question is an analogue of the well-known Erd0s similarity problem. In this paper, we show that for each sequence of real numbers whose integer parts form a set of positive upper Banach density, one can explicitly construct such a set S that contains no affine copy of that sequence. Since there exist sequences of arbitrarily rapid growth that satisfy this condition, our result answers Kolountzakis and Papageorgiou's question in the affirmative. A key ingredient of our proof is a generalization of results by Amice, Kahane, and Haight from metric number theory. We also construct a set S with the required property--but with e E (1/2, 1)--that contains no affine copy of {2"}.