On the number of quintic fields

• 成果类型: Article
• 署名作者: Kable, AC; Yukie, A
• 署名单位: Oklahoma State University System; Oklahoma State University - Stillwater; Tohoku University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0391-2
• 发表日期: 2005
• 页码: 217-259
• 关键词: prehomogeneous vector-spaces; zeta-functions; CONVERGENCE; density; discriminants

摘要

We show that the number of quintic number fields whose discriminant does not exceed X in absolute value is bounded by a constant times X1+epsilon for any epsilon > 0. This may be compared with the conjecture that the number of such fields is asymptotic to a constant times X as X tends to infinity.