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On the critical zeros of the Riemann zeta function

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

Yongxiao Lin

时间

2025年11月17日 10:00 至 11:00

地点

Shuangqing-B627

摘要

This is joint with Brian Conrey, David Farmer, Chung-Hang Kwan, and Caroline Turnage-Butterbaugh. When studying the zeros of Riemann zeta function at a height $T$ up the critical strip one often multiplies zeta by a Dirichlet polynomial, called a mollifier, of length $T^\theta$ before averaging in order to neutralize the irregularities of zeta. Levinson in his 1974 Advances paper famously proved that at least $1/3$ of the zeros of zeta are on the critical line, by using a mollifier of length $T^\theta$ with $\theta<1/2$. Significant efforts in the literature have been devoted to refine and optimize Levinson's mollifer. We prove that Levinson’s method, as modified by Conrey, will in fact produce a positive proportion of critical zeros, regardless how short the mollifier is.