The pointwise behavior of Riemann's function

We present a new and simple method for the determination of the pointwise Holder exponent of Riemann's function P1nD1 n-2 sin(z n2x) at every point of the real line. In contrast to earlier approaches, where wavelet analysis and the theta modular group were needed for the analysis of irrational points, our method is direct and elementary, being only based on the following tools from number theory and complex analysis: the evaluation of quadratic Gauss sums, the Poisson summation formula, and Cauchy's theorem.