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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The research is supported by the National Natural Science Foundation of China (No. 11101096).
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Jin, Q., Deng, G. & Sun, D. Julia lines of general random dirichlet series. Czech Math J 62, 919–936 (2012). https://doi.org/10.1007/s10587-012-0074-x
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DOI: https://doi.org/10.1007/s10587-012-0074-x