On sequences of Dirichlet polynomials uniformly bounded on half planes (Q1314887)

For given \(0 \leq \lambda_ 0 < \lambda_ 1< \cdots < \lambda_ n \to \infty\) and Dirichlet polynomials \(\tau_ n(z) = \sum^ n_{\nu=0} a_{n \nu} e^{-\lambda_ \nu z}\) \((a_{n \nu} \in \mathbb{C})\) the author proves in Theorem 2 estimates for the coefficients \(a_{n \nu}\) in the case that \(\{\tau_ n\}\) is uniformly bounded on a region containing a half plane. Furthermore, with Theorem 3 he proves for \(\tau_ n (z)\) a Jentzsch type theorem containing a statement on `accumulation points of the zeros of the \(\tau_ n (z)\)'. Both theorems are based on Theorem 1 which says roughly spoken that the functions \(| \tau_ n (z)e^{\lambda_ nz} |\) have increasing behaviour with \(\text{Re} z\). Theorem 2 as well as Theorem 3 have an analogue of a known result in case of complex polynomials, that is for the \(A\)-transforms of the geometric sequence where \(A=(a_{n \nu})\) (see Theorem 3.1 and 4.1 in [Mitt. Math. Sem. Gießen 113, 70 p. (1974; Zbl 0325.40003)]).