Faculty of Physics - University of Bucharest

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FACULTY OF PHYSICS

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2024-11-22 2:10

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Conference: Bucharest University Faculty of Physics 2018 Meeting

Section: Theoretical Physics and Applied Mathematics

Title:

One hundred years of Romanian contributions to the geometry of polynomials

Authors:

Doru STEFANESCU

Affiliation:

University of Bucharest, Faculty of Physics, P.O. Box MG-11, Bucharest-Magurele, Romania

E-mail

doru.stefanescu@gmail.com

Keywords:

geometry of polynomials, localization, bounds for roots

Abstract:

We present the main results obtained by Romanian Mathematicians concerning the localization of the roots of univariate polynomials with complex or real coefficients. We remind theorems of Dimitrie Pompeiu, Petre Sergescu, Theodor Angheluta and Tiberiu Popoviciu and also some results of contemporary mathematicians. We propose new bounds for positive roots that improve some results of Sergescu and Lagrange.

References:

1. D. Stefanescu, New bounds for positive roots of polynomials, J. Univ. Comp. Sci., 2132-2141 (2005).

2. P. Batra, M. Mignotte, D. Stefanescu, Improvements of Lagrange’s bound for polynomial roots, J. Symb. Comp., 82, 19–25 (2017).

3. D. Stefanescu, Early Romanian Contributions to Algebra and Polynomials, 39–47, in Mathematics almost everywhere, in memory of Solomon Marcus, World Scientific, Singapore (2017).