A short note on a conjecture of Okounkov about a q-analogue of multiple zeta values

TL;DR

This paper explores a specific q-analogue of multiple zeta values introduced by Okounkov, comparing it to generating functions for multiple divisor sums, and proposes a new conjecture on their dimensions supported by numerical evidence.

Contribution

It introduces a new conjecture on the dimensions of Okounkov's q-analogues, complementing existing conjectures and providing numerical evidence.

Findings

Comparison between Okounkov's q-analogues and divisor sum generating functions

Proposal of a new conjecture on the dimensions of these q-analogues

Numerical evidence supporting the conjecture

Abstract

In [Ok] Okounkov studies a specific $q$-analogue of multiple zeta values and makes some conjectures on their algebraic structure. In this note we compare Okounkovs $q$-analogues to the generating function for multiple divisor sums defined in [BK1]. We also state a conjecture on their dimensions that complements Okounkovs conjectural formula and present some numerical evidences for it.