Irreducible polynomials of bounded height
Lior Bary‐Soroker, Gady Kozma
Abstract
The goal of this paper is to prove that a random polynomial with independent and identically distributed random coefficients taking values uniformly in {1,…,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.
Topics & Concepts
MathematicsInfinityBounded functionPolynomialDegree (music)CombinatoricsIrreducible polynomialDiscrete mathematicsUniform boundednessGalois groupRandom elementPure mathematicsRandom variableMathematical analysisMatrix polynomialStatisticsAcousticsPhysicsAnalytic Number Theory ResearchGeometry and complex manifoldsAlgebraic Geometry and Number Theory