Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates are positive real numbers. We study the set ₂ of the quantities . We first show that √2 is the smallest point of ₂. Then, we prove that there exists a number l such that ₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of ₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm6221-1-2016,
author = {V. Flammang},
title = {The R2 measure for totally positive algebraic integers},
journal = {Colloquium Mathematicae},
volume = {144},
year = {2016},
pages = {45-53},
zbl = {06574990},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6221-1-2016}
}
V. Flammang. The R₂ measure for totally positive algebraic integers. Colloquium Mathematicae, Tome 144 (2016) pp. 45-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6221-1-2016/