Julia lines of general random dirichlet series |
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Authors: | Qiyu Jin Guantie Deng Daochun Sun |
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Institution: | 1. Campus de Tohaninic, Université de Bretagne-Sud, BP 573, 56017, Vannes, France 2. Université Européne de Bretagne, Bretagne, France 3. Key Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China 4. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, People’s Republic of China
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Abstract: | In this paper, we consider a random entire function f(s, ω) defined by a random Dirichlet series $\sum\nolimits_{n = 1}^\infty {{X_n}(w\omega ){e^{ - {\lambda _n}s}}} $ where X n are independent and complex valued variables, 0 ? λ n ↗ +∞. We prove that under natural conditions, for some random entire functions of order (R) zero f(s, ω) 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, ω) of order (R) zero, almost surely. |
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