A Generalization of the Schur-Siegel-Smyth Trace Problem

Kyle Pratt, George Shakan, Alexandru Zaharescu

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 consid…