Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

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
DOI: https://doi.org/10.1090/mcom/3518
Published electronically: February 18, 2020
MathSciNet review: 4109571
Full-text PDF
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 11C08, 11R06, 11Y40

Retrieve articles in all journals with MSC (2010): 11C08, 11R06, 11Y40


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
Email: valerie.flammang@univ-lorraine.fr

DOI: https://doi.org/10.1090/mcom/3518
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