The spectrum of singularities of Riemann’s function. (English) Zbl 0889.26005

Jaffard, Stéphane

Rev. Mat. Iberoam. 12, No. 2, 441-460 (1996).

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”.

Reviewer: V.Anisiu (Cluj-Napoca)

MSC:

26A27	Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
42C15	General harmonic expansions, frames
28A80	Fractals

Keywords:

Hölder regularity; Hausdorff dimension; wavelet; continued fractions; Riemann’s function