<abstract xmlns="http://www.w3.org/1999/xhtml">We provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form <italic>hdeg f · f(g/h)</italic>, where <italic>f, g, h</italic> are polynomials with integer coefficients, and <italic>g</italic> and <italic>h</italic> are relatively prime. The irreducibility conditions are expressed in terms of the prime factorization of the leading coefficient of the polynomial <italic>hdeg f</italic> · <italic>f(g/h)</italic>, the degrees of <italic>f, g, h</italic>, and the absolute values of their coefficients. In particular, by letting <italic>h =</italic> 1 we obtain irreducibility conditions for compositions of polynomials with integer coefficients.</abstract>

We provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form hdeg f · f(g/h), where f, g, h are polynomials with integer coefficients, and g and h are relatively prime. The irreducibility conditions are expressed in terms of the prime factorization of the leading coefficient of the polynomial hdeg f · f(g/h), the degrees of f, g, h, and the absolute values of their coefficients. In particular, by letting h = 1 we obtain irreducibility conditions for compositions of polynomials with integer coefficients.

Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients

Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 2, P.O. Box 1-764, Bucharest 014700, Romania

Simion Stoilow Institute of Mathematics of the Romanian Academy, Research Unit 5, P.O. Box 1-764, Bucharest 014700, Romania

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We provide irreducibility criteria for multiplicative convolutions of polynomials with integer coefficients, that is, for polynomials of the form hdeg f ·...

Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients

Published Online: Dec 10, 2014

Page range: 73 - 84

Received: Aug 03, 2013

DOI: https://doi.org/10.2478/auom-2014-0007

Keywords
multiplicative convolution of polynomials, resultants, irreducible polynomials

© 2014 Anca Iuliana Bonciocat et. al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Irreducibility Criteria for Compositions and Multiplicative Convolutions of Polynomials with Integer Coefficients

Published Online: Dec 10, 2014

Page range: 73 - 84

Received: Aug 03, 2013

DOI: https://doi.org/10.2478/auom-2014-0007

Keywordsmultiplicative convolution of polynomials, resultants, irreducible polynomials

© 2014 Anca Iuliana Bonciocat et. al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
multiplicative convolution of polynomials, resultants, irreducible polynomials