The universality of zeta-functions with multiplicative coefficients

被引：5
|
作者：
Laurincikas, A [1 ]
Slezeviciene, R [1 ]
机构：
[1] Vilnius State Univ, Dept Math & Informat, LT-2006 Vilnius, Lithuania
来源：
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2002年 / 13卷 / 03期
关键词：
Dirichlet series; probability measure; random element; universality; weak convergence;
D O I：
10.1080/10652460290009088
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the paper the function Z(s) = Sigma(m=1)(infinity) g(m)m-s, Rs >1 , where g(m) is a multiplicative function from the class {\cal M-beta,M-theta(c(1), c(2)) is considered. It is proved that the function Z(s) is universal, i.e. any function continuous and non-vanishing on a compact subset K of the strip {s is an element of C : beta < Rs < 1} with connected complement and analytic in the interior of K can be uniformly on K approximated by translations of the function Z(s) .
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页码：243 / 257
页数：15
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