数学物理学报(英文版)
數學物理學報(英文版)
수학물이학보(영문판)
Acta Mathematica Scientia
2003年
3期
426-432
,共7页
Random Dirichlet series%characteristic function%Picard point
Kahane has studiedthe value distribution ofthe Gauss-Taylor series∑anXnzn,∞where{Xn}is a complex Gauss sequence and∑|an|2=∞.Inthis paper,by trans forming the right half plane into the unit disc and setting up some important inequalities,the value distribution of the Dirichlet series∑Xne- nS is studied where{Xn}is a sequence of some non-degenerate independent random variable satisfying conditions:EXn=0;∞E|Xn|2=+∞;An∈N,Xn or ReXn or ImXn of bounded density.There exists α＞0 such that An:α2E|Xn|2≤E2|Xn|＜+∞(the classic Gauss and Steinhaus random variables are special cases of such random variables).The important results are obtainedthat every point on the line Res=0 is a Picard point of the series withoutfinite exceptional value a.s..
