Generalized polynomials and an estimate of the number of roots

Authors

  • Alan Almeida Santos Universidade Federal de Sergipe

DOI:

https://doi.org/10.22481/exon.v1i1.18173

Keywords:

Theory of equations, Generalized polynomials

Abstract

We will define a new class of functions which extend the notion of polynomial in one variable and we will prove a interesting result about this functions, en effect, that the
number of positive roots of a such function is less than the quantity of monomials which appear in its expression.

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Author Biography

Alan Almeida Santos, Universidade Federal de Sergipe

Departamento de Matem´atica, DMAI, Campus Prof. Alberto Carvalho, UFS, 49500-000, Itabaiana, SE
E-mail: alan@ufs.br

References

D. N. Bernstein, “The number of roots of a system of equations”, Functional Analysis and its Applications, 9, 183-185, (1975).

J. V. Uspensky, “Theory of Equations”, McGraw-Hill Book Company Inc., New York, (1948).

M. Hampton & R. Moeckel, “Finiteness of relative equilibria of the four body problem”, Inventiones Mathematicae, 163, 289-312, (2006).

S. Smale, “Mathematical problems for the next century”. Math. Intell. 20, 715, (1998).

B. Sturmfels, “Solving systems of polynomial equations”. CBMS, 97, (2002).

W. Rudin, “Principles of mathematical analysis”. McGraw-Hill, Third Edition, New York, (1976)

Published

2010-06-30

How to Cite

SANTOS, Alan Almeida. Generalized polynomials and an estimate of the number of roots. Exatas Online, [S. l.], v. 1, n. 1, p. 1–5, 2010. DOI: 10.22481/exon.v1i1.18173. Disponível em: https://periodicos2.uesb.br/exon/article/view/18173. Acesso em: 2 oct. 2026.