A study on the comparison of classic results on the location of zeros of polynomials in the complex plane

• Grant number: 19/07440-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2019
• End date: January 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Vanessa Avansini Botta Pirani
• Grantee: Leonardo Vidal Rosa
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil

Abstract

The main purpose of this project is a study of classic results on the location of zeros of polynomials, focusing on those that determine circles or rings in the complex plane where all zeros are located. However, it is intended to make a comparison between some of the most famous results in the literature (such as Eneström-Kakeya's Theorem, Cauchy's Theorem and Pellet's Theorem, among others), in order to determine which results are more accurate for certain classes of polynomials when a comparison is possible.