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The Erdös-Kac theorem for additive arithmetical semigroups

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Abstract

We show that the Erdös-Kac theorem for additive arithmetical semigroups can be proved under the condition that the counting function of elements has the asymptotics G(n) = q n(A + O(1/(lnn)k) as n → ∞ with A > 0, q > 1, and arbitrary k ∈ ℕ and that P(n) = O(q n/n) for the number of prime elements of degree n. This improves a result of Zhang.

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Authors and Affiliations

  1. Universität Paderborn, Warburger Str. 100, D-33098, Paderborn, Deutschland

    S. Wehmeier

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  1. S. Wehmeier
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Translated from Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 429–439, July–September, 2007.

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Wehmeier, S. The Erdös-Kac theorem for additive arithmetical semigroups. Lith Math J 47, 352–360 (2007). https://doi.org/10.1007/s10986-007-0024-8

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  • DOI: https://doi.org/10.1007/s10986-007-0024-8

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