On the congruence of finite sums involving generalized harmonic numbers modulo $p^2$

Abstract

We investigate congruence relationships of particular finite sums involving generalized harmonic numbers. We suggest a simpler and more transparent method to analyse these sums and present several additional results for certain special cases.where r = σ + it is a complex variable. However, in the study of divisibility it is assumed that r is an integer.Consider the behaviour of finite sums of terms involving GHN in the form