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

Bachmann, Henrik; Takeyama, Yoshihiro; Tasaka, Koji

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

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Bachmann, Henrik
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4171/205
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1807.00411.pdf
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Citation

Bachmann, H., Takeyama, Y., & Tasaka, K. (2020). Special values of finite multiple harmonic q-series at roots of unity. In F. Chapoton, F. Fauvet, C. Malvenuto, & J.-Y. Thibon (Eds.), Algebraic combinatorics, resurgence, moulds and applications (CARMA). Vol. 2 (pp. 1-18). Berlin: European Mathematical Society.

Cite as: https://hdl.handle.net/21.11116/0000-0008-9E48-6

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.