Weierstrass functions in Zygmund's class

Consider the function f(x) = Sigma(+infinity) (-n)(n=0 b) g(b(n)x) where b > 1 and g is an almost periodic C-1,epsilon function. It is well known that the function f lives in the so- called Zygmund class. We prove that f is generically nowhere differentiable. This is the case in particular if the elementary condition g'( 0) not equal 0 is satisfied. We also give a sufficient condition on the Fourier coefficients of g which ensures that f is nowhere differentiable.