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arXiv · 1402.5430

Counting degenerate polynomials of fixed degree and bounded height

Artūras Dubickas·Min Sha
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Abstract

In this paper, we give sharp upper and lower bounds for the number of degenerate monic (and arbitrary, not necessarily monic) polynomials with integer coefficients of fixed degree $n \ge 2$ and height bounded by $H \ge 2$. The polynomial is called degenerate if it has two distinct roots whose quotient is a root of unity. In particular, our bounds imply that non-degenerate linear recurrence sequences can be generated randomly.

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Artūras Dubickas, Min Sha. 2014-02-21. Counting degenerate polynomials of fixed degree and bounded height. https://arxiv.org/abs/1402.5430

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