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arXiv · 1404.0155

About the Uniform Hölder Continuity of Generalized Riemann Function

F. Bastin·S. Nicolay·L. Simons
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Abstract

In this paper, we study the uniform Hölder continuity of the generalized Riemann function $R_{α,β}$ (with $α>1$ and $β>0$) defined by \[ R_{α,β}(x)=\sum_{n=1}^{+\infty}\frac{\sin(πn^βx)}{n^α},\quad x\in\mathbb{R}, \] using its continuous wavelet transform. In particular, we show that the exponent we find is optimal. We also analyse the behaviour of $R_{α,β}$ as $β$ tends to infinity.

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BibTeXRIS

F. Bastin, S. Nicolay, L. Simons. 2014-04-01. About the Uniform Hölder Continuity of Generalized Riemann Function. https://arxiv.org/abs/1404.0155

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