A Correlated Digital Sum Problem Associated with Sums of Three Squares

Let (n) be the error term associated with the asymptotic formulafor the counting function on the set of numbers that are sumsof three squares. By considering (n) as a correlated digitalsum and applying the method of H. Delange on ordinary digitalsums we give very precise information on the average value of(n) in terms of a periodic continuous nowhere differentiablefunction having an absolutely convergent Fourier series withcoefficients expressed in terms of the Hurwitz zeta function.