Self-reciprocal polynomials over finite fields.
Meyn, Helmut, Götz, Werner (1989)
Séminaire Lotharingien de Combinatoire [electronic only]
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Meyn, Helmut, Götz, Werner (1989)
Séminaire Lotharingien de Combinatoire [electronic only]
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Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat (2006)
Acta Arithmetica
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Henk Hollmann (1986)
Acta Arithmetica
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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.
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....
Pradipto Banerjee, Michael Filaseta (2010)
Acta Arithmetica
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Ulrich Schoenwaelder (1988)
Manuscripta mathematica
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Norris Sookoo (2000)
Archivum Mathematicum
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Orthogonality conditions and recurrence relations are presented for generalized Krawtchouk polynomials. Coefficients are evaluated for the expansion of an arbitrary polynomial in terms of these polynomials and certain special values for generalized Krawtchouk polynomials are obtained. Summations of some of these polynomials and of certain products are also considered.
Khodakhast Bibak, Igor E. Shparlinski (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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We estimate the number of possible degree patterns of k-lacunary polynomials of degree t < p which split completely modulo p. The result is based on a combination of a bound on the number of zeros of lacunary polynomials with some graph theory arguments.
L. Hajdu, R. Tijdeman (2003)
Acta Arithmetica
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P. N. Shrivastava (1977)
Publications de l'Institut Mathématique
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Andrzej Schinzel (1970)
Acta Arithmetica
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