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Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8


Author: V. Flammang
Journal: Math. Comp. 90 (2021), 379-388
MSC (2010): Primary 11C08, 11R06, 11Y40
DOI: https://doi.org/10.1090/mcom/3580
Published electronically: September 8, 2020
MathSciNet review: 4166465
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Abstract: Previously, we established lower bounds for the usual measures (trace, length, Mahler measure) of totally positive algebraic integers, i.e., all of whose conjugates are positive real numbers. We used the method of explicit auxiliary functions and we noticed that the house of most of the totally positive polynomials involved in our functions are bounded by 5.8. Thanks to this observation, we are able to use the same method and give upper bounds for the usual measures of totally positive algebraic integers with house bounded by this value. To our knowledge, theses upper bounds are the first results of this kind.


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Additional Information

V. Flammang
Affiliation: UMR CNRS 7502, IECL, Université de Lorraine, site de Metz, Département de Mathématiques, UFR MIM, 3 rue Augustin Fresnel BP 45112 57073 Metz cedex 3 France
MR Author ID: 360354
Email: valerie.flammang@univ-lorraine.fr

DOI: https://doi.org/10.1090/mcom/3580
Received by editor(s): April 21, 2020
Published electronically: September 8, 2020
Article copyright: © Copyright 2020 American Mathematical Society