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Julia lines of general random dirichlet series

Abstract: 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.
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    Journal2012_Julia lines of general random dirichlet series.pdf [Fulltext]
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