Positive definite n-regular quadratic forms

• 成果类型: Article
• 署名作者: Oh, Byeong-Kweon
• 署名单位: Sejong University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0068-8
• 发表日期: 2007
• 页码: 421-453
• 关键词: non-residue; lattices; REPRESENTATION

摘要

A positive definite integral quadratic form f is called n-regular if f represents every quadratic form of rank n that is represented by the genus of f. In this paper, we show that for any integer n greater than or equal to 27, every n-regular (even) form f is (even) n-universal, that is, f represents all (even, respectively) positive definite integral quadratic forms of rank n. As an application, we show that the minimal rank of n-regular forms has an exponential lower bound for n as it increases.