报告人：林永晓 (山东大学)

报告时间：2025年12月18日（星期四）16:00-17:30

报告地点：东32楼216室

报告摘要：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.

邀请人：张庆