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On the Distribution of Polynomial Discriminants: Totally Real Case

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Abstract

We study the distribution of the discriminant D(P) of polynomials P from the class Pn(Q) of all integer polynomials of degree n and height at most Q. We evaluate the asymptotic number of polynomials P ∈ Pn(Q) having all real roots and satisfying the inequality |D(P)| ≤ X as Q→∞and X/Q2n−2→ 0.

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  1. Institute of Mathematics, National Academy of Sciences of Belarus, 220072, Minsk, Belarus

    Denis V. Koleda

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  1. Denis V. Koleda
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Correspondence to Denis V. Koleda.

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Dedicated to Professors Antanas Laurinˇcikas and Eugenijus Manstavičius on the occasion of their 70th birthdays

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Koleda, D.V. On the Distribution of Polynomial Discriminants: Totally Real Case. Lith Math J 59, 67–80 (2019). https://doi.org/10.1007/s10986-019-09434-z

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