A generalization of Dirichlet's unit theorem
A generalization of Dirichlet's unit theorem
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DOI：
10.4064/aa162-4-3
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发表时间：
2012-10
期刊：
影响因子：
0.7
通讯作者：
Paul Fili;Zachary Miner
中科院分区：
文献类型：
--
作者：
Paul Fili;Zachary Miner
我们将Dirichlet的S-单位定理从数域K上的S-单位的通常群推广到S上的所有代数数的无限秩群上，这些代数数的非平凡赋值仅在S上的位置上。具体地说，我们证明了代数S-单位的组模挠是一个Q-向量空间，当赋范的Weil高度，跨越一个超平面的产品公式，并在这个向量空间的元素是线性无关的Q保持其线性无关R。
We generalize Dirichlet’s S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a Q-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over Q retain their linear independence over R.