数域调节器的判别式下界

IF 0.3 4区数学 Q4 MATHEMATICS Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-12-31 DOI:10.5802/jtnb.1245

S. Akhtari, J. Vaaler

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引用次数: 0

摘要

我们证明了比较数域的调节器与其绝对判别式的不等式。我们在1984年西尔弗曼的工作中改进了一些想法，在那里这些一般不等式首次被证明。为了证明我们的主要定理，我们将这些改进与作者最近关于数域扩展中相对单位高度积的边界的结果结合起来。

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Lower bounds for regulators of number fields in terms of their discriminants

We prove inequalities that compare the regulator of a number field with its absolute discriminant. We refine some ideas in Silverman's work in 1984 where such general inequalities are first proven. In order to prove our main theorems, we combine these refinements with the authors' recent results on bounding the product of heights of relative units in a number field extension.

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