The spectrum of singularities of Riemann's function
For the Riemann's function \(\varphi (x)=\sum_{n=1}^\infty \frac 1{n^2}\sin \pi n^2x,\) the spectrum of singularities \(d(\alpha )\) is determined, where \(d(\alpha )\) denotes the Hausdorff dimension of the set of points and \(\varphi \) is Hölder-regular of order \(\alpha\). Furthermore, \(d\) satisfies the so called ``multifractal formalism for functions''.
scientific article; zbMATH DE number 933290