Abstract
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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Research of the first author was partially supported by the National Science Foundation. The third author was partially supported by KRF Research Fund (2003-070-C00001).
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Chan, W.K., Kim, B.M., Kim, MH. et al. Extensions of representations of integral quadratic forms. Ramanujan J 17, 145–153 (2008). https://doi.org/10.1007/s11139-007-9023-y
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DOI: https://doi.org/10.1007/s11139-007-9023-y