The central limit theorem for R.C. Baker sequences

Let D = (omega (n))(n greater than or equal to0) be the multiplicative semi-group generated by the coprime integers q1,...,q(tau) arranged in increasing order. If f is a real-valued 1-periodic function, we consider the sums S(n)f (t) = Sigma (0 less than or equal tok<n) f(<omega>(k)t). For a large class of functions, we prove the existence of a limiting variance sigma (2) for the sequence {Snf/rootn} we give a function characterization for the case when sigma = 0 and finally we prove a central limit theorem.