On the zetafunction of an arithmetical semigroup

被引：1
|
作者：
Warlimont, R [1 ]
机构：
[1] Univ Witwatersrand, John Knopfmacher Ctr Applicable Anal & Number The, ZA-2050 Wits, South Africa
来源：
MATHEMATISCHE ZEITSCHRIFT | 2003年 / 245卷 / 03期
关键词：
Power Series; Dirichlet Series; Arithmetical Semigroup;
D O I：
10.1007/s00209-003-0534-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Zetafunction Z of an additive, multiplicative arithmetical semigroup is a power series with radius of convergence rho(0less than or equal torholess than or equal to1), a Dirichlet series with abscissa of convergence alpha(0less than or equal toalphaless than or equal toinfinity), respectively.Conditions are given which ensure that rho>0 and Z(rho)=infinity, alpha<infinity and Z(alpha)=infinity hold true, respectively.
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页码：419 / 434
页数：16
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