Jaffard, Stéphane The spectrum of singularities of Riemann’s function. (English) Zbl 0889.26005 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) Cited in 50 Documents 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 PDF BibTeX XML Cite \textit{S. Jaffard}, Rev. Mat. Iberoam. 12, No. 2, 441--460 (1996; Zbl 0889.26005) Full Text: DOI EuDML OpenURL