Multiple Rogers--Ramanujan type identities for torus links

TL;DR

This paper derives multiple Rogers--Ramanujan type identities for zeta functions related to (2,2k) torus links, confirming a conjecture and exploring their properties.

Contribution

It introduces simple k-fold summation formulas for Quot and motivic Cohen--Lenstra zeta functions of torus links, leading to new identities and finitizations.

Findings

Established k-fold summation expressions for zeta functions.

Derived Rogers--Ramanujan type identities and their finitizations.

Confirmed a conjecture of Huang and Jiang.

Abstract

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.