Counting degenerate polynomials of fixed degree and bounded height

Artūras Dubickas, Min Sha*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
1 Downloads (Pure)

Abstract

In this paper, we give sharp upper and lower bounds for the number of degenerate monic (and arbitrary, not necessarily monic) polynomials with integer coefficients of fixed degree n ≥2 and height bounded by ≥2. The polynomial is called degenerate if it has two distinct roots whose quotient is a root of unity. In particular, our bounds imply that non-degenerate linear recurrence sequences can be generated randomly.

Original languageEnglish
Pages (from-to)517-537
Number of pages21
JournalMonatshefte fur Mathematik
Volume177
Issue number4
DOIs
Publication statusPublished - 25 Aug 2015
Externally publishedYes

Keywords

  • Degenerate polynomial
  • Linear recurrence sequence
  • Mahler measure
  • Resultant

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