A Generalization of a Theorem of Boyd and Lawton
This thesis applies to study first, in part 1, the Mahler measure of polynomials in one variable. It starts by giving some definitions and results that are important for calculating this height.        It also addresses the topic of Lehmer’s question, an interesting conjecture in the field, and it gives some examples and results aimed at resolving the issue.        The extension of the Mahler measure to several variable polynomials is then considered including  the subject of limit points with some examples.        In the second part, we first give definitions of a higher order for the Mahler measure, and generalize from single variable polynomials to multivariable polynomials.        Lehmer’s question has a counterpart in the area of the higher Mahler measure, but with totally different answers.        At the end, we reach our goal, where we will demonstrate the generalization of a theorem of Boyd-Lawton. This theorem shows a relation between the limit of Mahler measure of multivariable polynomials with Mahler measure of polynomials in one variable.  This result has implications in terms of Lehmer's conjecture and serves to clarify the relationship between the Mahler measure of one variable polynomials, and the Mahler measure of multivariable polynomials, which are very different.
higher Mahler measure Lehmer’s question Llimit points Multivariable polynomials Boyd-Lawton theorem