The Riemann Hypothesis and Stein's Method

Qi-Man Shao  (The Chinese University of Hong Kong)

14:00 pm - 15:00 pm, May 4th, 2016    Science Building A1510
             (闵行校区数学楼 401 同步视频直播)


The Rieman hypothesis is a well-known open question and there are many equivalent statements. One equivalent conjecture is that the moment generating function of a special probability density function, say $\Psi$, has pure imaginary zeros. So the conjecture is reduced to find a sequence of random variables whose moment generating functions have pure imaginary zeros and their limiting probability density function is $\Psi$. It was proved by Lee-Yang (1952) that the moment generating function of Ising models has pure imaginary zeros. Therefore, if one can find a sequence of Ising models so that the limiting probability density function is $\Psi$, then the Riemann Hypothesis holds.

In this talk we shall use Stein's method to give a concrete approach to identify the limiting distribution for any given sequence of Ising models. The problem can be reduced to calculate conditional expectations and conditional variances.

About the speaker:

邵启满教授为 ICM 45分钟报告人(2010)、香港中文大学教授、浙江大学教授。


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