We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8253-1-2016,
author = {Shabnam Akhtari and Jeffrey D. Vaaler},
title = {Heights, regulators and Schinzel's determinant inequality},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {285-298},
zbl = {06545353},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8253-1-2016}
}
Shabnam Akhtari; Jeffrey D. Vaaler. Heights, regulators and Schinzel's determinant inequality. Acta Arithmetica, Tome 172 (2016) pp. 285-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8253-1-2016/