Abstract
We consider random polynomials with independent identically distributed coefficients with a fixed law. Assuming the Riemann hypothesis for Dedekind zeta functions, we prove that such polynomials are irreducible and their Galois groups contain the alternating group with high probability as the degree goes to infinity. This settles a conjecture of Odlyzko and Poonen conditionally on RH for Dedekind zeta functions.
Funding Statement
E. B. acknowledges support from ERC Grant no. 617129 ‘GeTeMo’. P. V. acknowledges support from the Royal Society.
Citation
Emmanuel Breuillard. Péter P. Varjú. "Irreducibility of random polynomials of large degree." Acta Math. 223 (2) 195 - 249, December 2019. https://doi.org/10.4310/ACTA.2019.v223.n2.a1
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