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arXiv · 2011.06234

Approximately half of the roots of a random Littlewood polynomial are inside the disk

Oren Yakir
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Abstract

We prove that for large $n$, all but $o(2^{n})$ polynomials of the form $P(z) = \sum_{k=0}^{n-1}\pm z^k$ have $n/2 + o(n)$ roots inside the unit disk. This solves a problem from Hayman's book 'Research Problems in Function Theory' (1967).

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Oren Yakir. 2020-11-12. Approximately half of the roots of a random Littlewood polynomial are inside the disk. https://doi.org/10.4064/sm201117-28-1

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