A q-analogue of symmetric multiple zeta value

TL;DR

This paper introduces a q-analogue of symmetric multiple zeta values, preserving key algebraic relations and extending the classical theory with new q-deformed structures.

Contribution

It constructs a q-analogue of symmetric multiple zeta values satisfying double shuffle relations and related algebraic properties.

Findings

The q-analogue satisfies the inverse relation.

It obeys a part of the double shuffle relation.

It adheres to the Ohno-type relation.

Abstract

We construct a q-analogue of truncated version of symmetric multiple zeta values which satisfies the double shuffle relation. Using it, we define a q-analogue of symmetric multiple zeta values and see that it satisfies many of the same relations as symmetric multiple zeta values, which are the inverse relation and a part of the double shuffle relation and the Ohno-type relation.