On a certain class of infinite products with an application to arithmetical semigroups

DOI10.1007/BF01200088zbMath0708.11041OpenAlexW1983416860MaRDI QIDQ920141

Karl-Heinz Indlekofer, Richard Warlimont, Eugenijus Manstavicius

Publication date: 1991

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01200088

zbMATH Keywords

arithmetical semigroupsabstract prime number theorem

Mathematics Subject Classification ID

Dirichlet series, exponential series and other series in one complex variable (30B50) Zeta and (L)-functions: analytic theory (11M99)

Related Items (16)

On Labeled and Unlabeled Combinatorial Structures ⋮ RECENT DEVELOPMENTS AND APPLICATIONS OF ABSTRACT ANALYTIC NUMBER THEORY ⋮ JOHN KNOPFMACHER, [ABSTRACT ANALYTIC NUMBER THEORY, AND THE THEORY OF ARITHMETICAL FUNCTIONS] ⋮ ANALYTIC AND PROBABILISTIC THEORY OF ADDITIVE ARITHMETICAL SEMIGROUPS ⋮ DISTRIBUTION OF MULTIPLICATIVE FUNCTIONS DEFINED ON SEMIGROUPS ⋮ Dynamics on the number of prime divisors for additive arithmetic semigroups ⋮ Summation of values of multiplicative functions on semigroups ⋮ Generalizations of Alladi's formula for arithmetical semigroups ⋮ A Relationship between two Sequences and Arithmetical Semigroups ⋮ Asymptotic density in quasi-logarithmic additive number systems ⋮ Mean behaviour of multiplicative functions on additive arithmetical semigroups ⋮ Remarks on the number theory over additive arithmetical semigroups ⋮ Unnamed Item ⋮ Arithmetical semigroups. II: Sieving by large and small prime elements. Sets of multiples ⋮ Arithmetical semigroups. I: Direct factors ⋮ Tauberian Theorems for Sequences linked by a Convolution

Cites Work

• Unnamed Item
• The abstract prime number theorem for function fields
• The function field abstract prime number theorem

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