Mattarei, Sandro
(2007)
*Root multiplicities and number of nonzero coefficients of a polynomial.*
Journal of Algebra and Its Applications, 06
(03).
pp. 469-475.
ISSN 0219-4988

Full content URL: http://dx.doi.org/10.1142/S0219498807002338

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Item Type: | Article |
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Item Status: | Live Archive |

## Abstract

It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial over a field of characteristic zero is larger than the multiplicity of any of its nonzero roots. We extend this result to an appropriate statement in positive characteristic. Furthermore, we present a new proof of the original result, which produces also the exact number of monic polynomials of a given degree for which the bound is attained. A similar argument allows us to determine the number of monic polynomials of a given degree, multiplicity of a given nonzero root, and number of nonzero coefficients, over a finite field of characteristic larger than the degree.

Keywords: | polynomial, weight, root multiplicity |
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Divisions: | College of Science > School of Mathematics and Physics |

ID Code: | 18510 |

Deposited On: | 15 Feb 2017 16:45 |

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