Tag Archives: Alex Smith

Check the arXiV regularly!

Posted on February 18, 2023 by Persiflage

In a previous post, I discussed a new result of Smith which addressed the following question: given a measure \(\mu\) on \(\mathbf{R}\) supported on some finite union of intervals \(\Sigma\), under what conditions do there exist polynomials of arbitrarily large … Continue reading →

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Schur-Siegel-Smyth-Serre-Smith

Posted on November 25, 2021 by Persiflage

If \(\alpha\) is an algebraic number, the normlized trace of \(\alpha\) is defined to be \( \displaystyle{T(\alpha):=\frac{\mathrm{Tr}(\alpha)}{[\mathbf{Q}(\alpha):\mathbf{Q}].}}\) If \(\alpha\) is an algebraic integer that is totally positive, then the normalized trace is at least one. This follows from the AM-GM … Continue reading →

Posted in Mathematics | Tagged , , , , , | 5 Comments