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Mathematics of Computation

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An analog to the Schur-Siegel-Smyth trace problem

Author: V. Flammang
Journal: Math. Comp. 89 (2020), 2387-2398
MSC (2010): Primary 11C08, 11R06, 11Y40
Published electronically: February 18, 2020
MathSciNet review: 4109571
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Abstract: If $ \alpha $ denotes a totally positive algebraic integer of degree $ d$, i.e., its conjugates $ \alpha _1=\alpha , \ldots , \alpha _d$ are positive real numbers, we define $ {\mathrm {S}}_k(\alpha )= \sum _{i=1}^{d} \alpha _i^k$. $ {\mathrm {S}}_1(\alpha )$ is the usual trace of $ \alpha $ and has been studied by many authors throughout the years. In this paper, we focus our attention on the values of $ {\mathrm {S}}_2(\alpha )$, and our purpose is to establish for $ {\mathrm {S}}_2$ the same kinds of results as for the trace.

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Additional Information

V. Flammang
Affiliation: UMR CNRS 7502, IECL, Université de Lorraine, Département de Mathématiques, UFR MIM, 3 rue Augustin Fresnel, BP 45112 57073 Metz cedex 3, France

Received by editor(s): September 19, 2019
Received by editor(s) in revised form: December 4, 2019
Published electronically: February 18, 2020
Article copyright: © Copyright 2020 American Mathematical Society