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

By Fr'ed'eric Bayart, Daniel Pellegrino, J. B. Seoane-Sep'ulveda. 2013

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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.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6bf9632a99a2a887125a90b8496cbf08603dbf8a