Borel lines of random Dirichlet series (Q1599839)

The author has considered a random Dirichlet series \[ f(z,w)= \sum^\infty_{n=0} a_n z_n(\omega) e^{-\lambda_n s} \] and has established sufficient conditions such that \(f(z,w)\) is an almost surely entire function of order (R) infinite and for any \(t_0\in \mathbb{R}\), \(\forall\eta> 0\) and \(\forall\alpha\in\mathbb{C}\) \[ \limsup_{\sigma\to-\infty} {\log^+\#\{s: f(s,w)=\alpha, s\in\{s:|\text{Re }s\geq \sigma\}\cap \{s:|\text{Im }s- t_0|< \eta\}\}\over -\sigma}=+\infty, \] where \(\log^+ u=\log u\) if \(u\geq 1\) and \(0\) if \(u< 1\).