学术报告报告主题: Diophantine approximation via integer bases
报 告 人: Gerardo González Robert 博士（澳大利亚乐卓博大学（北京））
报告时间: 2024年 8月22日（星期四）上午10:00-11:00
报告地点: 4号楼318
邀 请 人: 李兵 教授
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数学8297至尊品牌游戏官方网站
2024年 8月 21日
报告摘要：
Classical Diophantine approximation studies how close can we approach to real numbers by rationals. A variant of this problem is to restrict the denominators of the approximating rationals to a subset of the natural numbers. In this talk, I will consider approximation by $b$-ary rationals where $b$ is a fixed natural number at least $2$. First, I will present a result relating approximation properties with respect to one base with asymptotic properties with respect to other bases. Afterwards, I will present some observations in the spirit of Lochs' Theorem in order to motivate a new exponent of approximation similar to the ones studied by Amou-Bugeaud and Bugeaud-Liao. This talk is based on a collaboration with Mumtaz Hussain and Simon Kristensen and with Mumtaz Hussain, Nikita Shulga, and Zhengliang Zhang.