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 H ≥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 language | English |
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Pages (from-to) | 517-537 |
Number of pages | 21 |
Journal | Monatshefte fur Mathematik |
Volume | 177 |
Issue number | 4 |
DOIs | |
Publication status | Published - 25 Aug 2015 |
Externally published | Yes |
Keywords
- Degenerate polynomial
- Linear recurrence sequence
- Mahler measure
- Resultant