Degree Name

MS (Master of Science)


Mathematical Sciences

Date of Award


Committee Chair or Co-Chairs

Robert Gardner

Committee Members

Anant Godbole, Rodney Keaton


The well known Eneström-Kakeya Theorem states that: for P(z)=∑i=0n ai zi, a polynomial of degree n with real coefficients satisfying 0 ≤ a0 ≤ a1 ≤ ⋯≤ an, all zeros of P(z) lie in |z|≤1 in the complex plane. In this thesis, we will find inner and outer bounds in which the zeros of complex and quaternionic polynomials lie. We will do this by imposing restrictions on the real and imaginary parts, and on the moduli, of the complex and quaternionic coefficients. We also apply similar restrictions on complex polynomials with complex coefficients to give a bound on the number of zeros in a disk centered at the origin. For each result, we will consider lacunary polynomials, that is polynomials of the form P(z)=a0+∑i=mn ai zi, as well as a new class of polynomials P(z)=a0+∑i=mm' ai zi + an zn.

Document Type

Thesis - unrestricted


Copyright by the authors.

Included in

Analysis Commons