Asymptotics for crank of overpartitions

This is the authors' abstract. We don't add key points for this paper.

Let M̄(a,c,n) denote the number of overpartitions of n with first residual crank congruent to a modulo c with c≥ 3 being odd and 0≤ a<c . The central objective of this paper is twofold: firstly, to establish an asymptotic formula for the crank of overpartitions; and secondly, to establish several inequalities concerning M̄(a,c,n) that encompasses crank differences, positivity, and strict log-subadditivity.