Dirichlet approximation and universal Dirichlet series

TL;DR

This paper characterizes the limits of Dirichlet polynomials on half-planes and extends classical approximation results to Dirichlet series, also strengthening the concept of universality in this context.

Contribution

It provides a comprehensive characterization of uniform limits of Dirichlet polynomials and extends classical approximation theorems to the Dirichlet setting, including universality.

Findings

Characterization of uniform limits of Dirichlet polynomials.

Approximation results analogous to Runge, Mergelyan, Vitushkin.

Strengthened notion of universal Dirichlet series.

Abstract

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.