Journal title
Annals of Mathematics
DOI
10.4007/annals.2020.192.3.6
Last updated
2024-04-25T08:16:36.573+01:00
Abstract
We show that there exist absolute constants $\Delta > \delta > 0$ such that,
for all $n \geqslant 2$, there exists a polynomial $P$ of degree $n$, with $\pm
1$ coefficients, such that $$\delta\sqrt{n} \leqslant |P(z)| \leqslant
\Delta\sqrt{n}$$ for all $z\in\mathbb{C}$ with $|z|=1$. This confirms a
conjecture of Littlewood from 1966.
for all $n \geqslant 2$, there exists a polynomial $P$ of degree $n$, with $\pm
1$ coefficients, such that $$\delta\sqrt{n} \leqslant |P(z)| \leqslant
\Delta\sqrt{n}$$ for all $z\in\mathbb{C}$ with $|z|=1$. This confirms a
conjecture of Littlewood from 1966.
Symplectic ID
1131645
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Publication type
Journal Article
Publication date
09 Nov 2020