  The main aim of this paper is to study the $n$-dimensional Bohr radius for
holomophic functions defined on 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
investigation 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
Bohr radius in terms of arithmetric Bohr radius.
