The number of extensions of a number field with fixed degree and bounded discriminant

• 成果类型: Article
• 署名作者: Ellenberg, Jordan S.; Venkatesh, Akshay
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.723
• 发表日期: 2006
• 页码: 723-741
• 关键词: galois-groups; density

摘要

We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant <= X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.