## 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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