A bound for the exterior product of S-units

IF 0.9 1区数学 Q2 MATHEMATICS Algebra & Number Theory Pub Date : 2024-09-19 DOI:10.2140/ant.2024.18.1589

Shabnam Akhtari, Jeffrey D. Vaaler

引用次数: 0

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 $S$ -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.

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S 单位外部积的边界

我们将 A. Schinzel 证明的实矩阵行列式不等式推广到欧几里得空间中更一般的向量外部积。我们将这一不等式应用于包含在数域 k 中的 S 单位的对数嵌入，从而得出以高的乘积表示的 S 单位外部乘积的约束。利用麦克马伦（P. McMullen）的一个体积公式，我们证明了我们的不等式在一个常数以内都是尖锐的，这个常数只取决于 S 单位群的秩，而不取决于域 k。我们的不等式与罗德里格斯-比列加斯（F. Rodriguez Villegas）的一个猜想有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

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