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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Algebraic integers whose conjugates all lie in an ellipse
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by Valérie Flammang and Georges Rhin PDF
Math. Comp. 74 (2005), 2007-2015 Request permission

Abstract:

We find all $15909$ algebraic integers $\boldsymbol {\alpha }$ whose conjugates all lie in an ellipse with two of them nonreal, while the others lie in the real interval $[-1,2]$. This problem has applications to finding certain subgroups of $SL(2,\mathbb {C})$. We use explicit auxiliary functions related to the generalized integer transfinite diameter of compact subsets of $\mathbb {C}$. This gives good bounds for the coefficients of the minimal polynomial of $\boldsymbol {\alpha }.$
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Additional Information
  • Valérie Flammang
  • Affiliation: UMR CNRS 7122 Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France
  • MR Author ID: 360354
  • Email: flammang@poncelet.univ-metz.fr
  • Georges Rhin
  • Affiliation: UMR CNRS 7122 Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France
  • Email: rhin@poncelet.univ-metz.fr
  • Received by editor(s): December 19, 2003
  • Received by editor(s) in revised form: May 13, 2004
  • Published electronically: March 8, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 2007-2015
  • MSC (2000): Primary 11R04, 11Y40, 12D10
  • DOI: https://doi.org/10.1090/S0025-5718-05-01735-7
  • MathSciNet review: 2164108