2017
Том 69
№ 9

All Issues

Natural boundary of random Dirichlet series

Ding Xiaoqing, Xiao Yimin

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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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 7, pp 1129-1138.

Citation Example: Ding Xiaoqing, Xiao Yimin Natural boundary of random Dirichlet series // Ukr. Mat. Zh. - 2006. - 58, № 7. - pp. 997–1005.

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