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

http:; link.springer.de/link/service/journals/00605/bibs/0129003/01290227.htm

ISSN

n/a

Notes

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Abstract

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. ....

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Keywords