Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8
Copyright policy )Upper bounds for the usual measures of totally positive algebraic integers with house less than 5.8
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.
explicit auxiliary functions, PV-numbers and generalizations; other special algebraic numbers; Mahler measure, absolute trace, Algebraic number theory computations, totally positive algebraic integers, absolute length, Polynomials in number theory, absolute Mahler measure
explicit auxiliary functions, PV-numbers and generalizations; other special algebraic numbers; Mahler measure, absolute trace, Algebraic number theory computations, totally positive algebraic integers, absolute length, Polynomials in number theory, absolute Mahler measure
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