On the mean value formula of Dedekind sums (Q2735299)

The author investigates the mean value estimate of the Dedekind sum NEWLINE\[NEWLINES(h,k)= \sum_{a=1}^k ((a/k))((ah/k)),NEWLINE\]NEWLINE where \(h\) and \(k\) are positive integers, and \(((x))=0\) or \(x-[x]-1/2\) according as \(x\) is an integer or not. For odd \(n\), an asymptotic formula is established for \(\sum_{h=1, (h,k)=1}^k S^n(h,k)\) that generalizes the previous results of \textit{W.-P. Zhang} [J. Théor. Nombres Bordx. 8, 429-442 (1996; Zbl 0871.11033)] and of \textit{X. He} and \textit{W.-P. Zhang} [Acta Math. Sin., Engl. Ser. 15, No. 2, 245-254 (1999; Zbl 0941.11018)].