Pseudorandomness of the Ostrowski sum-of-digits function

For an irrational alpha is an element of(0, 1), we investigate the Ostrowski sum-of-digits function sigma(alpha). For alpha having bounded partial quotients and theta is an element of R \ Z, we prove that the function g : n bar right arrow e(theta sigma(alpha)(n)), where e(x) = e(2 pi ix), is pseudorandom in the following sense: for all r is an element of N the limit gamma(r) = lim(N ->infinity) 1/N Sigma(0 <= n<N) g(n + r)<(g(n))over bar> exists and we have lim(R ->infinity) 1/R Sigma(0 <= r<R) vertical bar gamma(r)vertical bar(2) = 0.