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Lithuanian Mathematical Journal

, Volume 59, Issue 1, pp 67–80 | Cite as

On the Distribution of Polynomial Discriminants: Totally Real Case

  • Denis V. KoledaEmail author
Article
  • 27 Downloads

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.

Keywords

polynomial discriminant totally real zeros conjugate algebraic numbers integer polynomials 

MSC

primary 11J25 secondary 11N45 11C08 65H04 26C10 

Notes

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Authors and Affiliations

  1. 1.Institute of Mathematics, National Academy of Sciences of BelarusMinskBelarus

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