论文标题
$ s $单位的外部产品的限制
A bound for the exterior product of $S$-units
论文作者
论文摘要
我们将A. schinzel证明的真实基质的决定因素推广到欧几里得空间中矢量的更通用的外部产品。我们将这种不平等应用于数字字段$ k $中包含的$ s $单位的对数嵌入。这导致了$ s $单位的外部产品的限制，该产品表示为高度的产品。使用P. McMullen的音量公式，我们表明我们的不平等现象急剧达到一个常数，仅取决于$ s $单位组的排名，但不取决于$ k $。我们的不平等与F. Rodriguez Villegas的猜想有关。
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.
