Harmonic Analysis of some arithmetical functions
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 on power series, naturally associated with the mentioned Hilbert spaces.
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