Testing degenerate polynomials

Cipu, Mihai; Diouf, Ismaïla; Mignotte, Maurice

doi:10.1007/s00200-011-0150-8

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2014

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Cited by 2 publications

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“…By adopting this terminology, we say that a polynomial f ∈ C[X] is degenerate if it has a pair of distinct roots whose quotient is a root of unity. Note that there already exist some methods for testing whether a given polynomial with integer coefficients is degenerate or not, see, e.g., [7]. In the sequel, all the polynomials we consider have integer coefficients except in few cases when this will be indicated explicitly.…”

Section: Introductionmentioning

confidence: 99%

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Counting degenerate polynomials of fixed degree and bounded height

Dubickas

Sha

2014

Monatsh Math

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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.

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Section: Introductionmentioning

confidence: 99%

“…, ξ ℓ are the conjugates of a root of unity ξ 1 of degree ℓ. Several other examples can be found in [7].…”

Section: Introductionmentioning

confidence: 99%