On the location of critical points for polynomials

Guangping Xiang, Purdue University

Abstract

The well-known Sendov Conjecture asserts that if all the zeros of a polynomial p lie in the closed unit disk then within unit distance of each zero there must be a critical point of p. In Chapter 2, this conjecture is verified for polynomials of degree less than or equal to eight or arbitrary degree with at most eight distinct zeros and degree $n\ge11.$ In Chapter 3 the existence of extremal polynomials for Smale's mean value conjecture and properties of these polynomials are proved. As an application, all extremal polynomials are found among polynomials with degree five and real critical points.

Degree

Ph.D.

Advisors

Brown, Purdue University.

Subject Area

Mathematics

COinS