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Parity of the Number of Irreducible Factors for Composite Polynomials
Zusammenfassung
Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields.
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@article{urn:nbn:de:hebis:34-2008080723156,
author={Kim, Ryul and Koepf, Wolfram},
title={Parity of the Number of Irreducible Factors for Composite Polynomials},
year={2008}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2008$n2008 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2008080723156 3000 Kim, Ryul 3010 Koepf, Wolfram 4000 Parity of the Number of Irreducible Factors for Composite Polynomials / Kim, Ryul 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2008080723156=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 08, 06 7136 ##0##urn:nbn:de:hebis:34-2008080723156
2008-08-07T09:38:22Z 2008-08-07T09:38:22Z 2008 urn:nbn:de:hebis:34-2008080723156 http://hdl.handle.net/123456789/2008080723156 137304 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Discriminant Swan’s theorem Composition Finite field 510 Parity of the Number of Irreducible Factors for Composite Polynomials Preprint Various results on parity of the number of irreducible factors of given polynomials over finite fields have been obtained in the recent literature. Those are mainly based on Swan’s theorem in which discriminants of polynomials over a finite field or the integral ring Z play an important role. In this paper we consider discriminants of the composition of some polynomials over finite fields. The relation between the discriminants of composed polynomial and the original ones will be established. We apply this to obtain some results concerning the parity of the number of irreducible factors for several special polynomials over finite fields. open access Kim, Ryul Koepf, Wolfram Mathematische Schriften Kassel ;; 08, 06 Mathematische Schriften Kassel 08, 06
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