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

Flammang, V.

doi:10.1090/mcom/3580

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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