Multiple Rogers--Ramanujan type identities for torus links

In this paper, we establish simple $k$-fold summation expressions for the Quot and motivic Cohen–Lenstra zeta functions associated with the $(2,2k)$ torus links. Such expressions lead us to some multiple Rogers–Ramanujan type identities and their finitizations, thereby confirming a conjecture of Huang and Jiang. Several other properties of the two zeta functions will be examined as well.