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）

（闵行校区数学楼 401 同步视频直播）

__Abstract:__

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.

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 千人计划 教授。

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