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

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