Positive definite n-regular quadratic forms

被引：0
作者：
Byeong-Kweon Oh
机构：
[1] Sejong University,Department of Applied Mathematics
来源：
Inventiones mathematicae | 2007年 / 170卷
关键词：
Quadratic Form; Root Lattice; Class Number; Lower Type; Minimal Rank;
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学科分类号：
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.
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页码：421 / 453
页数：32
相关论文
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