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

Bayart, F.Pellegrino, D.Seoane-Sepúlveda, Juan B.2023-06-192023-06-1920140001-870810.1016/j.aim.2014.07.029https://hdl.handle.net/20.500.14352/33847We 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.engThe Bohr radius of the $ n $-dimensional polydisk is equivalent to $\ sqrt {\ frac {\ log n}{n}} $journal articlehttp://www.sciencedirect.com/science/article/pii/S000187081400262Xhttp://arxiv.org/abs/1310.2834open access51Bohr radiusInterpolationBohnenblust–Hille inequalityMatemáticas (Matemáticas)12 Matemáticas