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arXiv · 1710.05165

Irreducible polynomials of bounded height

Lior Bary-Soroker·Gady Kozma
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Abstract

The goal of this paper is to prove that a random polynomial with i.i.d. random coefficients taking values uniformly in $\{1,\ldots, 210\}$ is irreducible with probability tending to $1$ as the degree tends to infinity. Moreover, we prove that the Galois group of the random polynomial contains the alternating group, again with probability tending to $1$.

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Lior Bary-Soroker, Gady Kozma. 2017-10-14. Irreducible polynomials of bounded height. https://doi.org/10.1215/00127094-2019-0047

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