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 of these results are q-extensions of the corresponding congruences for ordinary multiple harmonic sums obtained by the authors in a previous paper. We also establish duality congruences for multiple q-harmonic non-strict sums and a kind of duality for multiple q-harmonic strict sums. Finally, we pose a conjecture concerning two kinds of cyclic sums of multiple q-harmonic sums.
Hessami Pilehrood, K., Hessami Pilehrood, T., Tauraso, R. (2017). Some q-congruences for homogeneous and quasi-homogeneous multiple q-harmonic sums. RAMANUJAN JOURNAL, 43(1), 113-139 [10.1007/s11139-016-9879-9].
Some q-congruences for homogeneous and quasi-homogeneous multiple q-harmonic sums
Tauraso R
2017-01-01
Abstract
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 of these results are q-extensions of the corresponding congruences for ordinary multiple harmonic sums obtained by the authors in a previous paper. We also establish duality congruences for multiple q-harmonic non-strict sums and a kind of duality for multiple q-harmonic strict sums. Finally, we pose a conjecture concerning two kinds of cyclic sums of multiple q-harmonic sums.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.