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arXiv · 1404.0155

About the Uniform H\"older Continuity of Generalized Riemann Function

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

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

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

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