Arithmetic and Analysis of the series $\displaystyle { \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{x}{n} }$

Roger Gay; Ahmed Sebbar

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arXiv · 2009.14070

Arithmetic and Analysis of the series $\displaystyle { \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{x}{n} }$

Roger Gay·Ahmed Sebbar

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Abstract

In this paper we connect a celebrated theorem of Nyman and Beurling on the equivalence between the Riemann hypothesis and the density of some functional space in $ L^2(0, 1)$ to a trigonometric series considered first by Hardy and Littlewood. We highlight some of its curious analytical and arithmetical properties.

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Roger Gay, Ahmed Sebbar. 2020-09-27. Arithmetic and Analysis of the series $\displaystyle { \sum_{n=1}^{\infty} \frac{1}{n} \sin \frac{x}{n} }$. https://arxiv.org/abs/2009.14070

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