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Algebraic Combinatorics, Resurgence, Moulds and Applications (CARMA)

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

Henrik Bachmann^[1], Yoshihiro Takeyama^[2] and Koji Tasaka^[3]

(1) Nagoya University, Japan
(2) University of Tsukuba, Japan
(3) Aichi Prefectural University, Nagakute-shi, Aichi, Japan

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.

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