Some Remarks on Additive Arithmetical Semigroups |
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| Authors: | Indlekofer K.‐H. |
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| Affiliation: | (1) Faculty of Mathematics and Informatics, University of Padeborn, Warburger Str. 100, 33098 Paderborn, Germany |
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| Abstract: | Under weak conditions called axioms  and  , we prove Chebyshev type estimates and asymptotic formulas, respectively, for the prime elements in general additive arithmetical semigroups. As applications, we derive asymptotic laws for the mean behavior of prime divisor functions and of distinct degrees of prime factors. |
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| Keywords: | additive arithmetical semigroup prime factor Chebyshev estimate mean value arithmetic function |
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