A Generalization of the Schur-Siegel-Smyth Trace Problem

Let $α$ be a totally positive algebraic integer, and define its absolute trace to be $\frac{Tr(α)}{\text{deg}(α)}$, the trace of $α$ divided by the degree of $α$. Elementary considerations show that the absolute trace is always at least one, while it is plausible that for any $ε>0$, the absolute trace is at least $2-ε$ 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.

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