Article
MSC:
30B20,
30B50,
30D05,
30D20,
30D35,
60G99 | MR 3010248 | Zbl 1274.30106 | DOI: 10.1007/s10587-012-0074-x
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Keywords:
random Dirichlet series; order $(R)$; Julia lines; entire function
random Dirichlet series; order $(R)$; Julia lines; entire function
Summary:
In this paper, we consider a random entire function $f(s,\omega )$ defined by a random Dirichlet series $\sum \nolimits _{n=1}^{\infty }X_n(\omega ) {\rm e} ^{-\lambda _n s}$ where $X_n$ are independent and complex valued variables, $0\leq \lambda _n \nearrow +\infty $. 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.
References:
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