Displaying similar documents to “Factorisation of x N - q over Q”

Combinatorial Computations on an Extension of a Problem by Pál Turán

Gaydarov, Petar, Delchev, Konstantin (2015)

Serdica Journal of Computing

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Turan’s problem asks what is the maximal distance from a polynomial to the set of all irreducible polynomials over Z. It turns out it is sufficient to consider the problem in the setting of F2. Even though it is conjectured that there exists an absolute constant C such that the distance L(f - g) <= C, the problem remains open. Thus it attracts different approaches, one of which belongs to Lee, Ruskey and Williams, who study what the probability is for a set of polynomials ‘resembling’...

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

Borissov, Yuri, Ho Lee, Moon, Nikova, Svetla (2008)

Serdica Journal of Computing

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This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007. In this paper, we study the ratio θ(n) = λ2 (n) / ψ2 (n), where λ2 (n) is the number of primitive polynomials and ψ2 (n) is the number of irreducible polynomials in GF (2)[x] of degree n. Let n = ∏ pi^ri, i=1,..l be the prime factorization of n. We show that, for fixed l and ri , θ(n) is close to 1 and θ(2n) is not less than...

Irreducible polynomials with all but one zero close to the unit disk

DoYong Kwon (2016)

Colloquium Mathematicae

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We consider a certain class of polynomials whose zeros are, all with one exception, close to the closed unit disk. We demonstrate that the Mahler measure can be employed to prove irreducibility of these polynomials over ℚ.