Abstract
the series converges absolutely. In this paper we give a simpler definition (5) of the maximal region, a generalization (4) of the CauchyHadamard formula to give the distance from an interior point to the frontier of this region, and, as an application of this formula, a generalization (Theorem 2) of Hille's result. This contains a well known relation between the abscissas of simple and absolute convergence for Dirichlet series with positive exponents. It will be convenient to introduce the notation
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