On the Height of the Sylvester Resultant

Abstract

Let $n$ be a positive integer. We consider the Sylvester resultant of $f$ and $g,$ where $f$ is a generic polynomial of degree 2 or 3 and $g$ is a generic polynomial of degree $n.$ If $f$ is a quadratic polynomial, we find the resultant's height. If $f$ is a cubic polynomial, we find tight asymptotics for the resultant's height.