A dimension conjecture for q-analogues of multiple zeta values

TL;DR

This paper investigates q-analogues of multiple zeta values, proposing dimension conjectures for their graded spaces, inspired by classical zeta value conjectures, and explores their algebraic structure.

Contribution

It introduces a new framework for q-analogues of multiple zeta values, defining weight and depth, and formulates conjectures on the dimensions of their graded spaces.

Findings

Proposes dimension conjectures for q-analogues of multiple zeta values.

Establishes a parallel between q-analogues and classical multiple zeta value conjectures.

Provides a formal structure for analyzing the algebraic properties of these q-series.

Abstract

We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension conjectures for the spaces of their weight- and depth-graded parts, which have a similar shape as the conjectures of Zagier and Broadhurst-Kreimer for multiple zeta values.