Sur les processus arithmétiques liés aux diviseurs

For natural integer n, let Dn denote the random variable taking the values log d for ddividing n with uniform probability 1/τ(n). Then t → P(Dn nt ) (0 t 1) is anarithmetic process with respect to the uniform probability over the first N integers. It isknown from previous works that this process converges to a limit law and that the sameholds for various extensions. We investigate the generalized moments of arbitrary ordersfor the limit laws. We also evaluate the mean value of the two-dimensional distributionfunction P(Dn nu, D{n/Dn} nv).