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Khintchine’s theorem on manifolds

发布时间:2022-03-23 浏览量:59

时   间:  2022-03-23 14:30 — 15:30

地   点:  腾讯会议 APP()
报告人:  杨磊
单   位:  四川大学
邀请人:  郑骋
备   注:  Please go to https://voovmeeting.com or https://meeting.tencent.com to download Voov meeting or Tencent meeting Meeting link:https://meeting.tencent.com/dm/k9FkfibejLBz Meeting No.:127-351-681 Meeting password:618034
报告摘要:  

In this talk, we will prove the convergence part of Khintchine’s theorem on non-degenerate manifolds. This confirms a conjecture of Kleinbock and Margulis in 1998. Our approach uses geometric and dynamical ideas together with a new technique of `major and minor arcs'. In particular, we establish sharp upper bounds for the number of rational points of bounded height lying near `major arcs' and give explicit exponentially small bounds for the measure of `minor arcs'. This is joint work with Victor Beresnevich.