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

DoYong Kwon

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Displaying similar documents to “Irreducible polynomials with all but one zero close to the unit disk”

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An estimate for coefficients of polynomials in $L^{2}$ norm. II.

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Combinatorial Computations on an Extension of a Problem by Pál Turán

Gaydarov, Petar, Delchev, Konstantin (2015)

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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’...

Extention of Apolarity and Grace Theorem

Sendov, Blagovest, Sendov, Hristo (2013)

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MSC 2010: 30C10 The classical notion of apolarity is defined for two algebraic polynomials of equal degree. The main property of two apolar polynomials p and q is the classical Grace theorem: Every circular domain containing all zeros of p contains at least one zero of q and vice versa. In this paper, the definition of apolarity is extended to polynomials of different degree and an extension of the Grace theorem is proved. This leads to simplification of the conditions of...

Differential equations associated with generalized Bell polynomials and their zeros

Seoung Cheon Ryoo (2016)

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In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.

Growth of polynomials whose zeros are outside a circle

K. Dewan, Sunil Hans (2008)

Annales UMCS, Mathematica

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If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.

Integer Linear Programming applied to determining monic hyperbolic irreducible polynomials with integer coefficients and span less than 4

Souad El Otmani, Armand Maul, Georges Rhin, Jean-Marc Sac-Épée (2013)

Journal de Théorie des Nombres de Bordeaux

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In this work, we propose a new method to find monic irreducible polynomials with integer coefficients, only real roots, and span less than 4. The main idea is to reduce the search of such polynomials to the solution of Integer Linear Programming problems. In this frame, the coefficients of the polynomials we are looking for are the integer unknowns. We give inequality constraints specified by the properties that the polynomials should have, such as the typical distribution of their roots....