»ã±¨±êÌâ (Title)£ºMoments of ranks and cranks, and quotients of Eisenstein series and the Dedekind eta function (ÖȺÍÓàÖȵľء¢Eisenstein¼¶ÊýÓëDedekind Etaº¯ÊýµÄÉÌ)

»ã±¨ÈË (Speaker)£º ÍõÁùȨ ½ÌÊÚ£¨Î人´óѧ£©

»ã±¨¹¦·ò (Time)£º2022Äê8ÔÂ28ÈÕ(ÖÜÈÕ) 15:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒé £¨»áÒéID£º356998915 ÃÜÂ룺220828£©

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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.