Bohr and Rogosinski abscissas for ordinary Dirichlet series

TL;DR

This paper proves that the Bohr and Rogosinski abscissas for certain Dirichlet series are independent of the target domain and provides new estimates for these abscissas.

Contribution

It establishes the independence of these abscissas from the domain and derives new bounds for them.

Findings

Abscissas are domain-independent for Dirichlet series mapping into convex domains.

New estimates for Bohr and Rogosinski abscissas are obtained.

Results extend understanding of Dirichlet series in complex analysis.

Abstract

We prove that the abscissas of Bohr and Rogosinski for ordinary Dirichlet series, mapping the right half-plane into the bounded convex domain $G\subset \mathbb{C} $ are independent of the domain $G$. Furthermore, we obtain new estimates about these abscissas.