  Let $\alpha$ be a totally positive algebraic integer, and define its absolute
trace to be $\frac{Tr(\alpha)}{\text{deg}(\alpha)}$, the trace of $\alpha$
divided by the degree of $\alpha$. Elementary considerations show that the
absolute trace is always at least one, while it is plausible that for any
$\epsilon >0$, the absolute trace is at least $2-\epsilon$ with only finitely
many exceptions. This is known as the Schur-Siegel-Smyth trace problem. Our aim
in this paper is to show that the Schur-Siegel-Smyth trace problem can be
considered as a special case of a more general problem.
