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BIMSA-YMSC Tsinghua Number Theory Seminar
On the critical zeros of the Riemann zeta function
On the critical zeros of the Riemann zeta function
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Yongxiao Lin
Time
Monday, November 17, 2025 10:00 AM - 11:00 AM
Venue
Shuangqing-B627
Abstract
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.