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Natural boundary of random Dirichlet series

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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.

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Authors and Affiliations

  1. Northwestern Polytechnical University, Xi’an, China

    X. Ding

  2. Michigan State University, East Lansing, USA

    Y. Xiao

Authors
  1. X. Ding
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  2. Y. Xiao
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Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 7, pp. 997–1005, July, 2006.

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Ding, X., Xiao, Y. Natural boundary of random Dirichlet series. Ukr Math J 58, 1129–1138 (2006). https://doi.org/10.1007/s11253-006-0124-3

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  • DOI: https://doi.org/10.1007/s11253-006-0124-3

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