Natural boundary of random Dirichlet series
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 con...
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| Date: | 2006 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2006
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/3509 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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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