About the Uniform Hölder Continuity of Generalized Riemann Function
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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