报告题目 (Title)：Moments of ranks and cranks, and quotients of Eisenstein series and the Dedekind eta function (秩和余秩的矩、Eisenstein级数与Dedekind Eta函数的商)
报告人 (Speaker)： 王六权 教授（武汉大学）
报告时间 (Time)：2022年8月28日(周日) 15:00
报告地点 (Place)：腾讯会议 （会议ID：356998915 密码：220828）
邀请人(Inviter)：陈旦旦
主办部门：理学院数学系
报告摘要：
Atkin and Garvan introduced the functions $N_k(n)$ and $M_k(n)$, which denote the $k$-th moments of ranks and cranks in the theory of partitions. We relate these functions to the quotients of Eisenstein series and the Dedekind eta function. Through the theory of modular forms, we establish congruences modulo arbitrary powers of some primes for the moments and symmetrized moments of ranks and cranks. As a byproduct, we obtain similar congruences for the higher order $\spt$-functions. This talk is based on a joint work with Yifan Yang.
