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ON AN ERDÓS SIMILARITY PROBLEM IN THE LARGE
作者:      发布时间:2023-11-29       点击数:
报告时间 2023-12-04 10时-12时 报告地点 zoom:894 9350 1808
报告人 YUVESHEN


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 SR such that |SI|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"}.



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