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arXiv · 1511.08837

A Generalization of the Schur-Siegel-Smyth Trace Problem

Kyle Pratt·George Shakan·Alexandru Zaharescu
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Abstract

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.

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Kyle Pratt, George Shakan, Alexandru Zaharescu. 2015-11-27. A Generalization of the Schur-Siegel-Smyth Trace Problem. https://arxiv.org/abs/1511.08837

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