Paley Effect for Entire Dirichlet Series

被引：0

作者：

Hlova, T. Ya. ^{[1
]}

Filevych, P. V. ^{[2
]}

机构：

[1] Ukrainian Natl Acad Sci, Inst Appl Problems Mech & Math, Lvov, Ukraine

[2] Stefanyk Precarpathian Natl Univ, Ivano Frankivsk, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2015年 / 67卷 / 06期

关键词：

Entire Function; Nonnegative Integer; Positive Function; Dirichlet Series; Maximum Modulus;

D O I：

10.1007/s11253-015-1117-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the entire Dirichlet series f(z) = a (n = 0) (a) a (n) e (z lambda n) , we establish necessary and sufficient conditions on the coefficients a (n) and exponents lambda(n) under which the function f has the Paley effect, i.e., the condition lim sup (r ->+infinity) ln M-f(r)/T-f(r) =+infinity is satisfied, where M (f) (r) and T (f) (r) are the maximum modulus and the Nevanlinna characteristic of the function f, respectively.

引用

页码：838 / 852

页数：15

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