Everywhere divergence of one-sided ergodic hilbert transform
For a given number α ϵ (0, 1) and a 1-periodic function f, we study the convergence of the series Σ∞ n=1f(x+nα)/n, called one-sided Hilbert transform relative to the rotation x → x + α mod 1. Among others, we prove that for any non-polynomial function of class C2 having Taylor-Fourier series (i.e. Fourier coefficients vanish on ℤ-), there exists an irrational number α (actually a residual set of α