Modeling the Dirichlet distribution using multiplicative functions

For q, m, n , d is an element of N and some multiplicative function f >= 0, we denote by T-3(n) the sum of f (d) over the ordered triples (q, m, d) with qmd = 12. We prove that Cesaro mean of distribution functions defined by means of T-3 uniformly converges to the one-parameter Dirichlet distribution function. The parameter of the limit distribution depends on the values of f on primes. The remainder term is estimated as well.