Results on the Number of Zeros in a Disk for Three Types of Polynomials
Document Type
Article
Publication Date
1-1-2016
Description
We impose a monotonicity condition with several reversals on the moduli of the coefficients of a polynomial. We then consider three types of polynomials: (1) those satisfying the condition on all of the coefficients, (2) those satisfying the condition on the even indexed and odd indexed coefficients separately, and (3) polynomials of the form P(z) = a0+ Σnj=µ ajzj where µ ≥ 1 with the coefficients aµ; aµ+1;…; an satisfying the condition. For each type of polynomial, we give a result which puts a bound on the number of zeros in a disk (in the complex plane) centered at the origin. For each type, we give an example showing the results are best possible.
Citation Information
Bryant, Derek; and Gardner, Robert. 2016. Results on the Number of Zeros in a Disk for Three Types of Polynomials. Acta et Commentationes Universitatis Tartuensis de Mathematica. Vol.20(2). 135-149. https://doi.org/10.12697/ACUTM.2016.20.12 ISSN: 1406-2283