Counting degenerate polynomials of fixed degree and bounded height

Artūras Dubickas, Min Sha*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
1 Downloads (Pure)


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
Issue number4
Publication statusPublished - 25 Aug 2015
Externally publishedYes


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


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