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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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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DOI: https://doi.org/10.1007/s10986-019-09434-z