A bound for the exterior product of $S$-units

Autor:	Akhtari, Shabnam, Vaaler, Jeffrey D.
Rok vydání:	2020
Předmět:	Mathematics - Number Theory
Druh dokumentu:	Working Paper
Popis:	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 $S$-units contained in a number field $k$. This leads to a bound for the exterior product of $S$-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 $S$-unit group but not on the field $k$. Our inequality is related to a conjecture of F. Rodriguez Villegas. Comment: Accepted for publication in Algebra & Number Theory. Previously cited as Heights, Regulators and Schinzel's determinant inequality, II
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.10857 Zobrazit plný text záznamu View this record from Arxiv