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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中文翻译：

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房子小于5.8的完全正代数整数的通常度量的上限

摘要：以前，我们为完全正代数整数的常规度量（迹线，长度，马勒度量）确定了下界，即所有其共轭都是正实数。我们使用了显式辅助函数的方法，并且我们注意到函数中涉及的大多数完全正多项式的房屋均以5.8为界。由于这一观察，我们能够使用相同的方法，并为以该值为边界的完全正代数整数的通常量度给出上限。据我们所知，这些上限是此类的第一个结果。

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