Logarithmic density and measures on semigroups

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Davenport and Erdös [3] proved that every set A of integers with the property that a ∈ A implies an ∈ A for all n (multiplicative ideal) has a logarithmic density. I generalized [5] this result to sets with the property that if for some numbers a, b, n we have a ∈ A, b ∈ A and an ∈ A, then necessarily bn ∈ A, which I call quasi-ideals. Here a new proof of this theorem is given, applying a result on convolution of measures on discretes semigroups. This leads to further generalizations, including an improvement of a result of Warlimont [8] on ideals in abstract arithmetic semigroups.

Original languageEnglish
Pages (from-to)307-317
Number of pages11
JournalManuscripta Mathematica
Issue number1
Publication statusPublished - Mar 1996

ASJC Scopus subject areas

  • Mathematics(all)

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