Special values of finite multiple harmonic q-series at roots of unity

TL;DR

This paper investigates special values of finite multiple harmonic q-series at roots of unity, revealing explicit evaluations and relations that connect to multiple zeta values and the Kaneko-Zagier conjecture.

Contribution

It provides new explicit evaluations and Ohno-Zagier-type relations for finite multiple harmonic q-series at roots of unity, advancing understanding of their structure.

Findings

Explicit evaluations of the series at roots of unity

Proof of Ohno-Zagier-type relations for these series

Connections to multiple zeta values and the Kaneko-Zagier conjecture

Abstract

We study special values of finite multiple harmonic q-series at roots of unity. These objects were recently introduced by the authors and it was shown that they have connections to finite and symmetric multiple zeta values and the Kaneko-Zagier conjecture. In this note we give new explicit evaluations for finite multiple harmonic q-series at roots of unity and prove Ohno-Zagier-type relations for them.