Extensions of representations of integral quadratic forms

被引:0
|
作者
Wai Kiu Chan
Byeong Moon Kim
Myung-Hwan Kim
Byeong-Kweon Oh
机构
[1] Wesleyan University,Department of Mathematics and Computer Science
[2] Kangnung National University,Department of Mathematics
[3] Seoul National University,Department of Mathematical Science
[4] Sejong University,Department of Applied Mathematics
来源
The Ramanujan Journal | 2008年 / 17卷
关键词
Extension of representations; Integral quadratic forms; 11E12; 11E20;
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学科分类号
摘要
Let N and M be quadratic ℤ-lattices, and K be a sublattice of N. A representation σ:K→M is said to be extensible to N if there exists a representation ρ:N→M such that ρ|K=σ. We prove in this paper a local–global principle for extensibility of representation, which is a generalization of the main theorems on representations by positive definite ℤ-lattices by Hsia, Kitaoka and Kneser (J. Reine Angew. Math. 301:132–141, 1978) and Jöchner and Kitaoka (J. Number Theory 48:88–101, 1994). Applications to almost n-universal lattices and systems of quadratic equations with linear conditions are discussed.
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页码:145 / 153
页数:8
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