Harmonic Analysis of some arithmetical functions
Number Theory
2020-09-30 v1 Complex Variables
Abstract
We study three functions which are power series in the variable , Dirichlet series in the variable 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 on power series, naturally associated with the mentioned Hilbert spaces.
Cite
@article{arxiv.2009.14069,
title = {Harmonic Analysis of some arithmetical functions},
author = {Roger Gay and Ahmed Sebbar},
journal= {arXiv preprint arXiv:2009.14069},
year = {2020}
}