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

### Impacto

Bayart, F. and Pellegrino, D. and Seoane-Sepúlveda, Juan B. (2014) The Bohr radius of the $n$-dimensional polydisk is equivalent to $\ sqrt {\ frac {\ log n}{n}}$. Advances in mathematics, 264 . pp. 726-746. ISSN 0001-8708

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http://arxiv.org/abs/1310.2834Organisation

## 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.

Item Type: Article Bohr radius; Interpolation; Bohnenblust–Hille inequality Sciences > Mathematics 29049 05 Mar 2015 09:56 28 Nov 2016 09:27