Moments of ranks and cranks, and Quotients of Eisenstein Series and the Dedekind Eta Function

Liuquan Wang, Yifan Yang

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. Let $e_{2r}(n)$ be the $n$-th Four…