Julia lines of general random dirichlet series

作者：Jin, Qiyu^*; Deng, Guantie; Sun, Daochun

来源：Czechoslovak Mathematical Journal, 2012, 62(4): 919-936.

DOI：10.1007/s10587-012-0074-x

• random Dirichlet series
• order (R)
• Julia lines
• entire function

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.

• 单位
  北京师范大学; 华南师范大学