Andrews-Beck Type Congruences for Overpartitions

Abstract

We prove Andrews-Beck type congruences for overpartitions concerning the $D$-rank and $M_2$-rank. To prove congruences, we establish the generating function for weighted $D$-rank (respectively, $M_2$-rank) moment of overpartitions and find a connection with the second $D$-rank (respectively, $M_2$-rank) moment for overpartitions.