Properties of Trinomials of Height at least 2

This paper is concerned with trinomials of the form $z^{n}+az^{m}+b$, where $0<m<n$ are relatively prime integers and $a$ and $b$ are non-zero complex numbers. Typically (but not exclusively), $a$ will be an integer with $|a| \geq 2$, while $b=\pm 1$. Our main results cover the irreducibility, Mahler measure and house of such trinomials.