Root multiplicities and number of nonzero coefficients of a polynomial

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

Full text not available from this repository.

Item Type:Article
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
Divisions:College of Science > School of Mathematics and Physics
ID Code:18510
Deposited On:15 Feb 2017 16:45

Repository Staff Only: item control page