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

July, 2022 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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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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Khodabakhsh HESSAMI PILEHROOD. Tatiana HESSAMI PILEHROOD. Roberto TAURASO. "On 3-2-1 values of finite multiple harmonic $q$-series at roots of unity." J. Math. Soc. Japan 74 (3) 753 - 758, July, 2022. https://doi.org/10.2969/jmsj/86238623

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Received: 14 January 2021; Published: July, 2022

First available in Project Euclid: 3 November 2021

MathSciNet: MR4484229

zbMATH: 1510.11135

Digital Object Identifier: 10.2969/jmsj/86238623

Subjects:

Primary: 11M32

Secondary: 05A30 , 11A07 , 11B65

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

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