Julia lines of general random dirichlet series

被引：6

作者：

Jin, Qiyu ^{[1
]}

Deng, Guantie ^{[2
]}

Sun, Daochun ^{[3
]}

机构：

[1] Univ Bretagne Sud, F-56017 Vannes, France

[2] Beijing Normal Univ, Sch Math Sci, Key Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

[3] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2012年 / 62卷 / 04期

基金：

中国国家自然科学基金;

关键词：

random Dirichlet series; order (R); Julia lines; entire function; VALUES;

D O I：

10.1007/s10587-012-0074-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a random entire function f(s, omega) defined by a random Dirichlet series where X (n) are independent and complex valued variables, 0 a (c) 1/2 lambda (n) a dagger u +a. We prove that under natural conditions, for some random entire functions of order (R) zero f(s, omega) almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J.R.Yu: Julia lines of random Dirichlet series. Bull. Sci. Math. 128 (2004), 341-353, by relaxing condition on the distribution of X (n) for such function f(s, omega) of order (R) zero, almost surely.

引用

页码：919 / 936

页数：18

共 17 条

[1]

DAVIES PL, 1973, P LOND MATH SOC, V26, P99

[2] Picard points of random Dirichlet series [J].

Ding, XQ ;

Yu, JR .

BULLETIN DES SCIENCES MATHEMATIQUES, 2000, 124 (03) :225-238

[3]

Kahane JP., 1985, SOME RANDOM SERIES F

[4]

LITTLEWOOD JE, 1949, ANN MATH, V50, P990, DOI 10.2307/1969591

[5]

Nevanlinna R, 1929, Le Theoreme de Picard-Borel et la Theorie des Fonctions Meromorphes

[6]

PALEY REA, 1930, P CAMBRIDGE PHILOS S, V26, P458

[7]

Paley REAC, 1932, P CAMB PHILOS SOC, V28, P190

[8]

Paley REAC, 1930, P CAMB PHILOS SOC, V26, P337

[9]

SUN DC, 1989, CR ACAD SCI I-MATH, V308, P205

[10]

SUN DC, 1990, CHINESE ANN MATH B, V11, P33

← 1 2 →