Irreducibility of random polynomials of large degree
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Breuillard, Emmanuel
Varju, Peter P
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.
Description
Keywords
math.NT, math.NT, math.PR, 11C08 (primary) and 11M41, 60J10 (secondary)
Journal Title
Acta Mathematica
Conference Name
Journal ISSN
0001-5962
1871-2509
1871-2509
Volume Title
223
Publisher
International Press
Publisher DOI
Rights
All rights reserved
Sponsorship
Royal Society (UF140146)
European Research Council (617129)
European Research Council (617129)
E. B. acknowledges support from ERC Grant no. 617129 `GeTeMo'. P. V. acknowledges support from the Royal Society.