论文标题
普遍的POHST不平等和小监管机构
Generalized Pohst inequality and small regulators
论文作者
论文摘要
当前使用小调节器的数字字段分类的方法主要取决于判别物的上限，可以通过在超立方体上寻找特定多项式函数的最佳上限来改进。在本文中，我们为领域的情况提供了新的和有效的上限，其中一个复杂的嵌入和五个至九之间：这是通过调整我们为研究完全真实案例所采取的策略来完成的，但是对于这种新环境，必须克服一些新的计算问题。结果，我们检测到具有最小调节器的签名（6,1）的四个数字字段；我们还在签名（3,1），（4,1）和（5,1）中扩展了具有小调节器的当前数字字段列表。
Current methods for the classification of number fields with small regulator depend mainly on an upper bound for the discriminant, which can be improved by looking for the best possible upper bound of a specific polynomial function over an hypercube. In this paper, we provide new and effective upper bounds for the case of fields with one complex embedding and degree between five and nine: this is done by adapting the strategy we have adopted to study the totally real case, but for this new setting several new computational issues had to be overcome. As a consequence, we detect the four number fields of signature (6,1) with smallest regulator; we also expand current lists of number fields with small regulator in signatures (3,1), (4,1) and (5,1).
