Natural boundary of random Dirichlet series - Ding, Xiaoqing; Xiao, Yimin (Ukrains’kyi Matematychnyi Zhurnal, 2006)
For the random Dirichlet series$$\sum\limits_{n = 0}^∞ {X_n (ω )e^{ - sλ _n } } (s = σ + it \in \mathbb{C}, 0 = λ _0 < λ _n \uparrow ∞ )$$whose coefficients are uniformly nondegenerate independent random variables, we provide some explicit conditions for the line of convergence to be its natural boundary a.s.