Dirichlet approximation and universal Dirichlet series
  We characterize the uniform limits of Dirichlet polynomials on a right half plane. In the Dirichlet setting, we find approximation results, with respect to the Euclidean distance and {to} the chordal one as well, analogous to classical results of Runge, Mergelyan and Vitushkin. We also strengthen the notion of universal Dirichlet series. 
Richard Aron, Fr\'ed\'eric Bayart, Paul Gauthier, Manuel Maestre and   Vassili Nestoridis
math.CV