Natural boundary of random Dirichlet series

摘要

For the random Dirichlet series ∑_n=0~∞ X_n(ω)_e~-sλ_n (s = δ + it ∈ C, 0 = λ_o < λ_n ↑∞ ) 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.