Division and composition theorems in the ring of analytic Dirichlet series.

DOI10.5802/aif.2000zbMath1077.32002OpenAlexW2317141587MaRDI QIDQ1878466

Augustin Mouze, Frederic Bayart

Publication date: 20 August 2004

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2003__53_7_2039_0

zbMATH Keywords

Dirichlet seriesarithmetic ringslocal analytic geometry

Mathematics Subject Classification ID

Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dirichlet series, exponential series and other series in one complex variable (30B50) Analytic algebras and generalizations, preparation theorems (32B05)

Related Items (max. 100)

Harmonic Analysis of Some Arithmetical Functions ⋮ Dirichlet series from the infinite dimensional point of view ⋮ The Fréchet Schwartz Algebra of Uniformly Convergent Dirichlet Series ⋮ Dirichlet spaces and their composition operators

Cites Work

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• Hardy spaces of Dirichlet series and their composition operators
• The ring of number-theoretic functions
• When \(\varphi(f)\) convergent implies \(f\) is convergent
• Ordre, convergence et sommabilité de produits de séries de Dirichlet. (Order, convergence and summability of products of Dirichlet series.)
• The composition operators on the space of Dirichlet series with square summable coefficients
• The ring of analytic Dirichlet series is factorial
• On composite formal power series
• Division dans l'anneau des séries formelles à croissance contrôlée. Applications

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