Natural boundary of random Dirichlet series

  • Xiaoqing Ding
  • Yimin Xiao

Abstract

For the random Dirichlet series $$\sum\limits_{n = 0}^\infty {X_n (\omega )e^{ - s\lambda _n } } (s = \sigma + it \in \mathbb{C}, 0 = \lambda _0 < \lambda _n \uparrow \infty )$$ 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.
Published
25.07.2006
How to Cite
DingX., and XiaoY. “Natural Boundary of Random Dirichlet Series”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 7, July 2006, pp. 997–1005, https://umj.imath.kiev.ua/index.php/umj/article/view/3509.
Section
Research articles