数学科学学院学术报告[2023] 067号

(高水平大学建设系列报告838号）

报告题目: Visibility of lattice points in Polya's walk

报告人：卢美洁（山东大学）

报告时间：2023年10月17日10:00-11:00

报告地点：汇星楼（科技楼）501

报告内容：Visible lattice points is one of the important research objects in number theory. In the previous studies of classical analytic number theory, the density of the corresponding lattice points is considered from the deterministic point of view for various counting problems of visible lattice points. In this talk, we consider the visible points from the perspective of random walks. Precisely, we study the distribution of the visible lattice points in certain perturbed P\'{o}lya's walk on $\mathbb{Z}^k$, we prove that the density of visible lattice points in a perturbed P\'{o}lya's walk is almost surely $1/\zeta(k)$, where $\zeta(s)$ denotes the Riemann zeta function. This work combines tools from both number theory and probability theory.

报告人简历：卢美洁，山东大学数学学院博士研究生，研究方向为解析数论，已经在国际权威数论期刊Journal of Number Theory等期刊上发表了论文两篇。

欢迎师生参加！

邀请人：王英男

数学科学学院

2023年10月15日