数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (3): 426-.
• 论文 • 上一篇
田范基, 任耀峰
TIAN Fan-Ji, LIN Yao-Feng
摘要:
Kahane has studied the value distribution of the Gauss-Taylor series
∞∑n=0anXnzn,
where {Xn} is a complex Gauss sequence and
∞∑n=1|an|2=∞.
In this paper, by transforming the
right half plane into the unit disc and
setting up some important inequalities,
the value distribution of the Dirichlet series
∞∑n=0Xne−λnS
is studied where {Xn} is a sequence of some non-degenerate
independent random variable satisfying conditions:
EXn=0;∞∑n=0E|Xn|2=+∞;∀n∈N,Xn or ReXn or ImXn of bounded density.
There exists α>0 such that ∀n:α2E|Xn|2≤E2|Xn|<+∞ (the classic Gauss and Steinhaus random variables
are special cases of such random variables).
The important results are obtained that every point on the line Res=0 is
a Picard point of the series without finite exceptional value a.s..
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