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: f􀀀1 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].

Included in

Mathematics Commons

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