报告地点：行健楼学术活动室665
报告人简介：
林永晓，山东大学教授、博士生导师，国家级青年人才。主要研究方向为解析数论与自守形式。先后在J. Eur. Math. Soc., Amer. J. Math., Int. Math. Res. Not.等国际著名学术期刊发表多篇论文。
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.
