Some $q$-congruences for homogeneous and quasi-homogeneous multiple $q$-harmonic sums

Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood, Roberto Tauraso

We show some new Wolstenholme type $q$-congruences for some classes of multiple $q$-harmonic sums of arbitrary depth with strings of indices composed of ones, twos and threes. Most…