On the distribution of polynomials with bounded height

Csanád Bertók, Lajos Hajdu, Attila Pethő

Published 2016-11-24Version 1

We provide an asymptotic expression for the probability that a randomly chosen polynomial with given degree, having integral coefficients bounded by some B, has a prescribed signature. We also give certain related formulas and numerical results along this line. Our theorems are closely related to earlier results of Akiyama and Peth\H{o}, and also yield extensions of recent results of Dubickas and Sha.