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The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.

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In this article we investigate the number A (t) of lattice points in x/t ~ where is a convex body in R s (s/> 3) which has a smooth boundary with nonzero Gaussian curvature throughout, and t is a large real parameter. We establish an asymptotic formula A (t) = Vt s/2 + 0 (t x(s~) (V the volume of ~) which improves upon a classic result of E. HLAWXA [5].