On the number of polynomials of bounded height that satisfy the Dumas criterion

Randell Heyman

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1 Citation (Scopus)

Abstract

We study integer coefficient polynomials of fixed degree and maximum height H that are irreducible by the Dumas criterion. We call such polynomials Dumas polynomials. We derive upper bounds on the number of Dumas polynomials as H → ∞. We also show that, for a fixed degree, the density of Dumas polynomials in the set of all irreducible integer coefficient polynomials is strictly less than 1.
Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalJournal of Integer Sequences
Volume17
Issue number2
Publication statusPublished - 2014

Keywords

  • Coprimality
  • Dumas criterion
  • Irreducible polynomial

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