Arithmetic Bohr radius for the Minkowski space

TL;DR

This paper investigates the arithmetic Bohr radius for holomorphic functions on Reinhardt domains in complex spaces, linking it to classical Bohr radius and Minkowski space geometry.

Contribution

It establishes a connection between classical and arithmetic Bohr radii and determines their exact values in Minkowski spaces.

Findings

Connected classical and arithmetic Bohr radii in Minkowski spaces.

Derived the exact value of the Bohr radius in terms of the arithmetic Bohr radius.

Extended understanding of holomorphic functions on Reinhardt domains.

Abstract

The main aim of this paper is to study the arithmetic Bohr radius for holomophic functions defined on a Reinhardt domain in $\mathbb{C}^n$ with positive real part. The present investigation is motivated by the work of Lev Aizenberg [Proc. Amer. Math. Soc. 128 (2000), 2611--2619]. A part of our study in the present paper includes a connection between the classical Bohr radius and the arithmetic Bohr radius of unit ball in the Minkowski space $\ell^n_{q}\, , 1\leq q\leq \infty$. Further, we determine the exact value of a Bohr radius in terms of arithmetric Bohr radius.