Borel lines of Random Dirichlet series

The growth of Dirichlet series

“…By Theorem 1, we deduce Yu Chia-Yung's result [15], [13] as Corollary 1. Then we give Example 1 to show that the condition ∆ = 0 is much less restrictive than the condition lim n→+∞ n/λ n < +∞, which implies that the Dirichlet series acts more or less like a power series.…”

“…When σ u = 0, by the method of J. Ritt [6], Yu Chia-Yung [15], [13] defined the order and type of f (s) under the conditions lim n→+∞ ln |a n | λ n = 0 and lim n→+∞ n λ n < +∞, and obtained some results between the growth of f (s) and the coefficients, which extends some of G. Valiron's results [9]. In this paper, we improve one of his results.…”

Julia lines of general random dirichlet series

“…First, we need the following lemma. [14]). Let {X n (ω)} be a sequence of non-degenerate, symmetric, and independent complex random variables and satisfy the conditions (17) and (18).…”

“…In [12], [13], the author obtained some important results on Dirichlet series convergent or convergent almost surely (a.s.) only in a half-plane. The related research has been extended to more general random Dirichlet series and more accurate results have been given in recent years (see [2], [8], [9], [10], [16]).…”

“…The related research has been extended to more general random Dirichlet series and more accurate results have been given in recent years (see [2], [8], [9], [10], [16]). For random entire functions defined by random Dirichlet series, there are some better results for functions a.s. of infinite order (R) [14]. Recently, J. R. Yu [15] gives a general result on some random entire functions a.s. of zero order (R) which does not contain a theorem of P. L. Davies [1].…”