报告题目 (Title)：The Beurling--Wintner problem and analytic number theory
中文标题：Beurling-Wintner问题与解析数论
报告人 (Speaker)：郭坤宇（复旦大学数学科学学院）
报告时间 (Time)：2023年11月30日(周四) 15:00
报告地点 (Place)：上海大学宝山校区GJ303
邀请人(Inviter)：席东盟、李晋、张德凯
报告摘要：This talk concerns a long-standing problem on completeness of function systems generated by odd periodic extensions of functions in $L^2(0,1)$. This problem, raised by Beurling and Wintner in the 1940s, is closely related to the Riemann Hypothesis. We completely solve the rational version of step functions (that is, those functions with rational jump discontinuities) by approaches from analytic number theory, and present several deep applications including a complete solution to the rational version of Kolzov completeness problem. This is a joint work with Dr. Hui Dan.