中科院数学与系统科学研究院
数学研究所
学术报告会
报告人： Prof. Qi-Man Shao(The Chinese University of Hong Kong)
题 目：The Riemann Hypothesis and Stein’s Method
时 间：2016.06.06（星期一），15 :00-16 :00
地 点：晨兴510室
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 Ψ, 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 Ψ. 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 Ψ, 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.
