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

2014/06/16 by Khodabakhsh Hessami Pilehrood, Pilehrood, Khodabakhsh Hessami, Tatiana Hessami Pilehrood +3
Mathematics · #11A07 #11B65 #30E05 #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.CO #msc:11A07 #msc:11B65 #msc:30E05

paper · pdf · doi:10.48550/arxiv.1406.4022

This article is based on the previous version, but the results have been reworked and extended substantially

openalex publication_date 2014/06/16 · arxiv created 2015/06/26 · arxiv updated 2015/06/29 · openalex created_date 2022/08/05 · openalex updated_date 2026/07/28

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. Finally, we pose a conjecture concerning two kinds of cyclic sums of multiple q-harmonic sums.

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