Boundary behaviour of Dirichlet series with applications to universal series

TL;DR

This paper explores how the boundary behaviour of Dirichlet series relates to the convergence of their partial sums, providing new insights into their approximation capabilities and boundary properties.

Contribution

It establishes new connections between boundary behaviour and convergence of Dirichlet series, with applications to universal approximation properties.

Findings

Boundary behaviour linked to partial sum convergence.

Insights into universal series approximation.

Enhanced understanding of Dirichlet series boundary properties.

Abstract

This paper establishes connections between the boundary behaviour of functions representable as absolutely convergent Dirichlet series in a half-plane and the convergence properties of partial sums of the Dirichlet series on the boundary. This yields insights into the boundary behaviour of Dirichlet series and Taylor series which have universal approximation properties.