New Relations Concerning a Mean Value of Some Hardy Sums and Ramanujan Sum.

Dedekind sum first occurred naturally in Dedekind's transformation law of his eta-function. In analogy, Hardy sums are encountered in the transformation formula of the theta function. Up to now, they have many of remarkable applications in analytic number theory (Dedekind's η-function), algebraic number theory (class numbers), lattice point problems, topology and algebraic geometry. Miscellaneous arithmetical properties of these sums have been analyzed by many scholars. Recently, considering the characteristics of Hardy sums and other celebrated sums such as Ramanujan sum and Kloosterman sum, interesting and meaningful identities have been obtained. In this paper, we continue to focus on arithmetical aspects of Hardy sums and Ramanujan sum. More precisely, we consider a mean value problem of these sums and Ramanujan sum with the help of the features of Dirichlet L-functions and present some computational formulas for them. [ABSTRACT FROM AUTHOR]