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arXiv · 1611.08128

On the distribution of polynomials with bounded height

Csanád Bertók·Lajos Hajdu·Attila Pethő
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Abstract

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.

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Csanád Bertók, Lajos Hajdu, Attila Pethő. 2016-11-24. On the distribution of polynomials with bounded height. https://arxiv.org/abs/1611.08128

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