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Algebraic integers whose conjugates all lie in an ellipse |
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| Authors: | Valé rie Flammang Georges Rhin. |
| Affiliation: | UMR CNRS 7122 Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France ; UMR CNRS 7122 Département de Mathématiques, UFR MIM, Université de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France |
| Abstract: | We find all  algebraic integers  whose conjugates all lie in an ellipse with two of them nonreal, while the others lie in the real interval ![$[-1,2]$](http://www.ams.org/mcom/2005-74-252/S0025-5718-05-01735-7/gif-abstract0/img3.gif){kind=small} . This problem has applications to finding certain subgroups of  . We use explicit auxiliary functions related to the generalized integer transfinite diameter of compact subsets of  . This gives good bounds for the coefficients of the minimal polynomial of  |
| Keywords: | Explicit auxiliary functions integer transfinite diameter. |
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