Positive density of integer polynomials with some prescribed properties

Arturas Dubickas, Min Sha*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In this paper, we show that various kinds of integer polynomials with prescribed properties of their roots have positive density. For example, we prove that almost all integer polynomials have exactly one or two roots with maximal modulus. We also show that for any positive integer n and any set of n distinct points symmetric with respect to the real line, there is a positive density of integer polynomials of degree n, height at most H and Galois group Sn whose roots are close to the given n points.

Original languageEnglish
Pages (from-to)27-44
Number of pages18
JournalJournal of Number Theory
Volume159
DOIs
Publication statusPublished - 1 Feb 2016
Externally publishedYes

Keywords

  • Dominant polynomial
  • Integer polynomial
  • Polynomial root
  • Positive density
  • Primary
  • Secondary

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