On q-Analog of Wolstenholme Type Congruences for Multiple Harmonic Sums

TL;DR

This paper explores q-analogs of multiple harmonic sums, establishing congruences using generating functions and shuffle relations, and extends the study to both homogeneous and non-homogeneous cases.

Contribution

It introduces new congruences for q-analogs of multiple harmonic sums at arbitrary depth, expanding on previous work by Dilcher.

Findings

Derived congruences for homogeneous q-harmonic sums

Applied generating functions and shuffle relations

Extended results to non-homogeneous cases

Abstract

Multiple harmonic sums are iterated generalizations of harmonic sums. Recently Dilcher has considered congruences involving q-analogs of these sums in depth one. In this paper we shall study the homogeneous case for arbitrary depth by using generating functions and shuffle relations of the q-analog of multiple harmonic sums. At the end, we also consider some non-homogeneous cases.