2020/09/27 by Roger Gay, Gay, Roger, Ahmed Sebbar +1
Mathematics · #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Meromorphic and Entire Functions #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2009.14069
openalex publication_date 2020/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Möbius 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.