#### Date of Award

2017

#### Document Type

Open Access Thesis

#### Department

Mathematics

#### Sub-Department

College of Arts and Sciences

#### First Advisor

Michael Filaseta

#### Abstract

A Newman polynomial is a polynomial with coefficients in f0;1g and with constant term 1. It is known that the roots of a Newman polynomial must lie in the slit annulus fz 2C: f1 1 such that if a polynomial f (z) 2 Z[z] has Mahler measure less than s and has no nonnegative real roots, then it must divide a Newman polynomial. In this thesis, we present a new upper bound on such a s if it exists. We also show that there are infinitely many monic polynomials that have distinct Mahler measures which all lie below f, have no nonnegative real roots, and have no Newman multiples. Finally, we consider a more general notion in which multiples of polynomials are considered in R[z] instead of Z[z].

#### Recommended Citation

Saunders, S. V.(2017). *Polynomials Of Small Mahler Measure With no Newman Multiples.* (Master's thesis). Retrieved from https://scholarcommons.sc.edu/etd/4369