## Electronic Theses and Dissertations

#### Degree Name

MS (Master of Science)

#### Program

Mathematical Sciences

5-2014

Robert Gardner

#### Committee Members

Jeff Knisley, Anant Godbole

#### Abstract

In this thesis, we put restrictions on the coefficients of polynomials and give bounds concerning the number of zeros in a specific region. Our results generalize a number of previously known theorems, as well as implying many new corollaries with hypotheses concerning monotonicity of the modulus, real, as well as real and imaginary parts of the coefficients separately. We worked with Enestr\"{o}m-Kakeya type hypotheses, yet we were only concerned with the number of zeros of the polynomial. We considered putting the same type of restrictions on the coefficients of three different types of polynomials: polynomials with a monotonicityflip" at some index $k$, polynomials split into a monotonicity condition on the even and odd coefficients independently, and ${\cal P}_{n,\mu}$ polynomials that have a gap in between the leading coefficient and the proceeding coefficient, namely the $\mu^{\mbox{th}}$ coefficient.

#### Document Type

Thesis - Open Access

COinS