Volume 281, Issue 9 pp. 1240-1253

Original Paper

A Capelli type theorem for multiplicative convolutions of polynomials

Anca Iuliana Bonciocat,

Corresponding Author

Anca Iuliana Bonciocat

[email protected]

Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1–764, RO-014700 Bucharest, Romania

Universität Bonn, Institut für Angewandte Mathematik, Abt. für Stochastik, Wegelerstr. 6, 53115 Bonn, Germany

Phone: +40 213 196 506, Fax: +40 213 196 505Search for more papers by this author

Nicolae Ciprian Bonciocat,

Nicolae Ciprian Bonciocat

[email protected]

Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1–764, RO-014700 Bucharest, Romania

Phone: +40 213 196 506, Fax: +40 213 196 505

Search for more papers by this author

Anca Iuliana Bonciocat,

Corresponding Author

Anca Iuliana Bonciocat

[email protected]

Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1–764, RO-014700 Bucharest, Romania

Universität Bonn, Institut für Angewandte Mathematik, Abt. für Stochastik, Wegelerstr. 6, 53115 Bonn, Germany

Phone: +40 213 196 506, Fax: +40 213 196 505Search for more papers by this author

Nicolae Ciprian Bonciocat,

Nicolae Ciprian Bonciocat

[email protected]

Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1–764, RO-014700 Bucharest, Romania

Phone: +40 213 196 506, Fax: +40 213 196 505

Search for more papers by this author

First published: 13 August 2008

https://doi.org/10.1002/mana.200510674

Citations: 6

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Abstract

We prove a Capelli type theorem on the canonical decomposition for multiplicative convolutions of polynomials. We derive then some irreducibility criteria for convolutions of polynomials in several variables over a given field. The irreducibility conditions are expressed only in terms of the degrees of the polynomials in convolution, the degrees of their coefficients, and the degrees of some suitable divisors of the resulting leading coefficient. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

References

[1] A. I. Bonciocat, and A. Zaharescu, Irreducibility results for compositions of polynomials in several variables, Proc. Indian Acad. Sci., Math. Sci. 115, No. 2, 117–126 (2005).
10.1007/BF02829621
Web of Science® Google Scholar
[2] N. C. Bonciocat, Upper bounds for the number of factors for a class of polynomials with rational coefficients, Acta Arith. 113, No. 2, 175–187 (2004).
10.4064/aa113-2-5
Web of Science® Google Scholar
[3] A. Capelli, Sulla riduttibilità delle equazioni algebriche, Nota prima, Rend. Accad. Sci. Fis. Mat. Soc. Napoli 3, 243–252 (1897).
Google Scholar
[4] M. Cavachi, On a special case of Hilbert's irreducibility theorem, J. Number Theory 82, No. 1, 96–99 (2000).
10.1006/jnth.1999.2476
Web of Science® Google Scholar
[5] M. Cavachi, M. Vâjâitu, and A. Zaharescu, A class of irreducible polynomials, J. Ramanujan Math. Soc. 17, No. 3, 161–172 (2002).
Google Scholar
[6] S. Lang, Algebra (Addison-Wesley Publ. Comp., Reading, Mass., 1965).
Google Scholar
[7] S. Lipka, Uber die Irreduzibilität von Polynomen, Math. Ann. 118, 235–245 (1941).
10.1007/BF01487363
Web of Science® Google Scholar
[8] O. Ore, Einige Bemerkungen über Irreduzibilität, Jahresber. Deutsch. Math.-Verein. 44, 147–151 (1934).
Google Scholar
[9] L. Rédei, Algebra, Vol. 1, translated from the Hungarian (Pergamon Press, Oxford, 1967).
Google Scholar
[10] A. Schinzel, Selected Topics on Polynomials (University of Michigan Press, Ann Arbor, 1982).
Google Scholar

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Volume281, Issue9

September 2008

Pages 1240-1253

A Capelli type theorem for multiplicative convolutions of polynomials

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A Capelli type theorem for multiplicative convolutions of polynomials

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