A bound for the exterior product of $S$-units
Number Theory
2023-10-23 v2
Abstract
We generalize an inequality for the determinant of a real matrix proved by A. Schinzel, to more general exterior products of vectors in Euclidean space. We apply this inequality to the logarithmic embedding of -units contained in a number field . This leads to a bound for the exterior product of -units expressed as a product of heights. Using a volume formula of P. McMullen we show that our inequality is sharp up to a constant that depends only on the rank of the -unit group but not on the field . Our inequality is related to a conjecture of F. Rodriguez Villegas.
Cite
@article{arxiv.2009.10857,
title = {A bound for the exterior product of $S$-units},
author = {Shabnam Akhtari and Jeffrey D. Vaaler},
journal= {arXiv preprint arXiv:2009.10857},
year = {2023}
}
Comments
Accepted for publication in Algebra & Number Theory. Previously cited as Heights, Regulators and Schinzel's determinant inequality, II