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

Khodabakhsh Hessami Pilehrood; Tatiana Hessami Pilehrood; Roberto Tauraso

doi:10.2969/jmsj/86238623

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

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

Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso

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Keywords: multiple harmonic sums, 𝑞-analogs, roots of unity

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2022 Volume 74 Issue 3 Pages 753-758

DOI https://doi.org/10.2969/jmsj/86238623

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Abstract

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

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