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

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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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Official URL: http://www.sciencedirect.com/science/article/pii/S000187081400262X


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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
Uncontrolled Keywords:Bohr radius; Interpolation; Bohnenblust–Hille inequality
Subjects:Sciences > Mathematics
ID Code:29049
Deposited On:05 Mar 2015 09:56
Last Modified:28 Nov 2016 09:27

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