2018
Том 70
№ 7

All Issues

Xiao Yimin

Articles: 1
Article (English)

Natural boundary of random Dirichlet series

Ding Xiaoqing, Xiao Yimin

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 7. - pp. 997–1005

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.