Ukrainian Mathematical Journal

, Volume 58, Issue 7, pp 1129–1138 | Cite as

Natural boundary of random Dirichlet series

  • X. Ding
  • Y. Xiao


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.


Independent Random Variable Dirichlet Series Natural Boundary Martingale Difference Convergence Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • X. Ding
    • 1
  • Y. Xiao
    • 2
  1. 1.Northwestern Polytechnical UniversityXi’anChina
  2. 2.Michigan State UniversityEast LansingUSA

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