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arXiv · 2009.14069

Harmonic Analysis of some arithmetical functions

Roger Gay·Ahmed Sebbar
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Abstract

We study three functions which are power series in the variable $z$, Dirichlet series in the variable $s$ and with coefficients given by arithmetical functions. A strong point is to relate these functions to some Hilbert spaces. Three main ingredients are used: an estimate of Davenport on sums of M\"obius functions, a result of Lucht on convolutions of arithmetical Dirichlet series and the introduction of an operation $\otimes$ on power series, naturally associated with the mentioned Hilbert spaces.

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Roger Gay, Ahmed Sebbar. 2020-09-27. Harmonic Analysis of some arithmetical functions. https://arxiv.org/abs/2009.14069

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