The Bohr radius of the $n$-dimensional polydisk is equivalent to $\sqrt{\frac{\log n}{n}}$

Abstract

We show that the Bohr radius of the polydisk ${\mathbb{D}}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$. Our argument is based on a new interpolative approach to the Bohnenblust--Hille inequalities which allows us to prove that the polynomial Bohnenblust--Hille inequality is subexponential.

The introduction was expanded and some misprints corrected

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