Julia lines of random Dirichlet series

Julia lines of general random dirichlet series

“…Our results are general and contain the results in [15]. Furthermore, let X ′ n (ω) = X(ω)/∆ n which are complex random variables of the same distribution, and |a n | = ∆ n .…”

“…We first recall some results of [15]. The author of [15] introduces a special random Dirichlet series…”

“…For random entire functions defined by random Dirichlet series, there are some better results for functions a.s. of infinite order (R) [14]. Recently, J. R. Yu [15] gives a general result on some random entire functions a.s. of zero order (R) which does not contain a theorem of P. L. Davies [1]. In this paper, the conditions of the theorems in [15] are found to be too strong.…”

“…In this paper, the conditions of the theorems in [15] are found to be too strong. By improving the method of the proof in [15], we discard the same distribution condition of the theorems in [15], and obtain the same results for a random entire function a.s. of zero order (R).…”

“…Recently, J. R. Yu [15] gives a general result on some random entire functions a.s. of zero order (R) which does not contain a theorem of P. L. Davies [1]. In this paper, the conditions of the theorems in [15] are found to be too strong. By improving the method of the proof in [15], we discard the same distribution condition of the theorems in [15], and obtain the same results for a random entire function a.s. of zero order (R).…”