Author Affiliation, Ana.
Department of Mathematics and Computer Science
The prime element theorem on additive arithmetic semigroups, II
Illinois Journal of Mathathematics
Date of Publication
In this paper, we give estimates for the remainders of the prime element theorems on additive arithmetical semigroups, which were proved with a remainder of o(1) form in the previous paper under the same title. The new estimates can be used in the investigation of mean-values of counterparts of classical arithmetic functions m(n) and l(n) in additive arithmetic semigroups. The investigation reveals an interesting situation in which theese counterparts do not have a mean-value. This phenomenon does not occur in the theory of the Beurling generalized integers. (AU)....