Distribution of orders in number fields
Distribution of orders in number fields
复制标题
订单在数字字段中的分布
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Ramin Takloo
中科院分区：
文献类型：
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作者：
N. Kaplan;Jake Marcinek;Ramin Takloo
摘要本文研究数域上有界判别式的阶分布。我们使用由Grunewald、Segal和Smith介绍的Zeta函数。为了开展我们的研究，我们使用了p-ADIVE和理据整合技术来分析Zeta函数。给出了五次数域的整数环中包含的阶数的一个渐近公式。我们还得到了高次数域的非平凡界。
AMS科目分类：初级11M41；11R29；次级11S40
AbstractIn this paper, we study the distribution of orders of bounded discriminants in number fields. We use the zeta functions introduced by Grunewald, Segal, and Smith. In order to carry out our study, we use p-adic and motivic integration techniques to analyze the zeta function. We give an asymptotic formula for the number of orders contained in the ring of integers of a quintic number field. We also obtain non-trivial bounds for higher degree number fields.
AMS Subject Classification: Primary 11M41; 11R29; secondary 11S40