Extensions of representations of integral quadratic forms |
| |
| Authors: | Wai Kiu Chan Byeong Moon Kim Myung-Hwan Kim Byeong-Kweon Oh |
| |
| Institution: | (1) Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06459, USA;(2) Department of Mathematics, Kangnung National University, Kangwondo, 210-702, Korea;(3) Department of Mathematical Science, Seoul National University, Seoul, 151-747, Korea;(4) Department of Applied Mathematics, Sejong University, Seoul, 143-747, Korea |
| |
| Abstract: | Let N and M be quadratic ?-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 ?-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. |
| |
| Keywords: | Extension of representations Integral quadratic forms |
| 本文献已被 SpringerLink 等数据库收录！ |
|
