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The main aim of this paper is to answer certain open questions related to theexact values of multidimensional Bohr radii by using the concept of arithmeticBohr radius for holomorphic functions defined in complete Reinhardt domains in$\mathbb{C}^n$ with values in complex Banach spaces. More specifically, forholomorphic functions with values in arbitrary complex Banach spaces, weexplore the asymptotic estimates of the arithmetic Bohr radius in the unit ballof $\ell^n_q$ $(1\leq q\leq \infty)$ spaces. As an application, we obtain theexact value of multidimensional Bohr radius for the unit ball in $\ell^n_1$spaces which improves the previously known result of Aizenberg.

Multidimensional Bohr radii for holomorphic functions with values in complex Banach spaces