On $3-2-1$ values of finite multiple harmonic $q$ -series at roots of unity

preprint2021arXivOpen access

We mainly answer two open questions about finite multiple harmonic $q$ -series on 3-2-1 indices at roots of unity, posed recently by H. Bachmann, Y. Takeyama, and K. Tasaka. Two conjectures regarding cyclic sums which generalize the given results are also provided.

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On $3-2-1$ values of finite multiple harmonic $q$ -series at roots of unity

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On 3−2−13-2-13−2−1 values of finite multiple harmonic qqq-series at roots of unity

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On $3-2-1$ values of finite multiple harmonic $q$ -series at roots of unity