On the distribution of polynomial discriminants: totally real case

2018/08/30 by Dzianis Kaliada, Kaliada, Dzianis
Mathematics · #11C08 #11J25 (Primary) #11N45 #26C10 (Secondary) #65H04 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1808.10414

openalex publication_date 2018/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• On the number of integral quadratic polynomials with bounded heights and discriminants

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