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Article overview
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A Generalization of the Schur-Siegel-Smyth Trace Problem | Kyle Pratt
; George Shakan
; Alexandru Zaharescu
; | Date: |
27 Nov 2015 | Abstract: | Let $alpha$ be a totally positive algebraic integer, and define its absolute
trace to be $frac{Tr(alpha)}{ ext{deg}(alpha)}$, 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. | Source: | arXiv, 1511.8837 | Services: | Forum | Review | PDF | Favorites |
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