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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
A chebyshev type upper estimate for prime elements in additive arithmetic semigroups
Medium Designator
n/a
Connective Phrase
n/a
Journal Title
Monatshefte für Mathematik
Translated Title
n/a
Reprint Status
Refereed
Date of Publication
2000
Volume ID
129
Issue ID
3
Page(s)
227-60
Language
n/a
Connective Phrase
n/a
Location/URL
Let G(n) and (n) be two sequences of nonnegative numbers which satisfy G(0)=1 and an additive convolution equation $(\Lambda {*} G)(n)=nG(n),n=0,1,2, \ldots$. A Chebyshev-type upper estimate for prime elements in an additive arithmetic semigroup is essentially a tauberian theorem on (n) and G(n). Suppose with real constants $0 \les \rho_1 < \cdots < \rho_r,\rho_r \ges 1, A_1, \ldots , A_r, A_r > 0$. The theorem proved here states that $\Lambda (n)\ll q^n$ and that $\sum_{m=1}^n\Lambda (m) q^{-m}=\rho_r n+R(n)+O(1)$ holds with an explicit function R(n) of order <1 in n. This theorem is sharp. It has several applications.....