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arXiv · 1808.10414

On the distribution of polynomial discriminants: totally real case

Dzianis Kaliada
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Abstract

In the paper we study the distribution of the discriminant $D(P)$ of polynomials $P$ from the class $\mathcal{P}_{n}(Q)$ of all integer polynomials of degree $n$ and height at most $Q$. We evaluate the asymptotic number of polynomials $P\in \mathcal{P}_{n}(Q)$ having all the roots real and satisfying the inequality $|D(P)|\le X$ as $Q\to\infty$ and $X/Q^{2n-2}\to 0$.

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Dzianis Kaliada. 2018-08-30. On the distribution of polynomial discriminants: totally real case. https://arxiv.org/abs/1808.10414

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