# Smoothness of Fourier series with polynomial frequencies

 Orateur: UBIS Adrian Localisation: Université autonome de Madrid, Espagne Type: Séminaire cristolien d'analyse multifractale Site: UPEC Salle: I1-223 Date de début: 17/01/2013 - 11:00 Date de fin: 17/01/2013 - 11:00

Let $P$ be any non-linear polynomial with integer coefficients. Consider the function defined by keeping just the Fourier coefficients of the ”fractional part” function whose frequencies are of the shape $P(n)$ with $n$ a natural number. We will show that the smoothness properties of this function are quite complex in the sense that for each s in some interval, the points with Holder exponent s form a set of positive Hausdorff dimension. This had been previously shown by S. Jaffard for $P$ a quadratic polynomial, namely for Riemann’s example of a continuous but almost nowhere differentiable function.