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Publication Type
Journal Article
UWI Author(s)
Author, Analytic
Zhang, Wen-Bin
Author Affiliation, Ana.
Department of Mathematics and Computer Science
Article Title
The prime element theorem on additive arithmetic semigroups, II
Medium Designator
n/a
Connective Phrase
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Journal Title
Illinois Journal of Mathathematics
Translated Title
n/a
Reprint Status
n/a
Date of Publication
1998
Volume ID
42
Issue ID
2
Page(s)
198-229
Language
n/a
Connective Phrase
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Location/URL
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ISSN
n/a
Notes
n/a
Abstract
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)....
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