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

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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.

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Authors and Affiliations

  1. The Fields Institute, 222 College Street, Toronto, ON, M5T 3J1, Canada

    Kh. Hessami Pilehrood & T. Hessami Pilehrood

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica, 00133, Rome, Italy

    R. Tauraso

Authors
  1. Kh. Hessami Pilehrood
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  2. T. Hessami Pilehrood
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  3. R. Tauraso
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Corresponding author

Correspondence to R. Tauraso.

Additional information

Kh. Hessami Pilehrood and T. Hessami Pilehrood acknowledge the support from the Fields Institute Research Immersion Fellowships.

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Hessami Pilehrood, K., Pilehrood, T.H. & Tauraso, R. Some q-congruences for homogeneous and quasi-homogeneous multiple q-harmonic sums. Ramanujan J 43, 113–139 (2017). https://doi.org/10.1007/s11139-016-9879-9

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  • DOI: https://doi.org/10.1007/s11139-016-9879-9

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