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

Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso

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 con…