On the reciprocity formula for generalized Dedekind sums (Q1825891)

The sums in the title are defined by \[ s(h,k,r)=\sum^{k}_{j=1}((j/k))((hj+r/k)), \] where h and k are integers, \(k>0\), r is a real number, \(((x))=x-[x]\) if \(x\neq integer\), and \(((x))=0\) otherwise. The author gives a new proof of the reciprocity law for these sums. He also relates these sums to a function introduced by \textit{T. Yoshida} [J. Algebra 118, No.2, 498-527 (1988; Zbl 0656.20008)] on a finite abelian group.