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

• ### Henrik Bachmann

Nagoya University, Japan
• ### Yoshihiro Takeyama

University of Tsukuba, Japan
• ### Koji Tasaka

Aichi Prefectural University, Nagakute-shi, Aichi, Japan

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## 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.