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| CONSTRUCTION OF INDECOMPOSABLE DEFINITE HERMITIAN FORMS |
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Citation： |
Zhu Fuzu.CONSTRUCTION OF INDECOMPOSABLE DEFINITE HERMITIAN FORMS[J].Chinese Annals of Mathematics B,1994,15(3):349~360 |
| Page view： 1046
Net amount： 864 |
Authors： |
Zhu Fuzu; |
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| Abstract： |
This paper gives a method to construct indecomposable positive definite
integral Hermitian forms over an imaginary quadratic field
$Q(\sqrt{-m})$ with given discriminant and given rank. It is shown that
for any natural numbers $n$ and $a$, there are $n$-ary indecomposable
positive definite integral Hermitian lattices over $Q(\sqrt{-1})$ (resp.
$Q(\sqrt{-2}))$ with discriminant $a$, except for four (resp. one)
exceptions. In these exceptional cases there are no lattices with the
desired properties. |
Keywords： |
Indecomposable lattice (form), Minimum of a lattice
(form), Minimal vector,Irreducible vector. |
Classification： |
11E41 |
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