On nondecomposable positive definite Hermitian forms over imaginary quadratic fields |
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Authors: | ZHU Fuzu |
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Institution: | Department of Mathematics, East China Normal University, |
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Abstract: | Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of
integers Rm of an imaginary quadratic field ℚ(√−m). Using our methods, one can construct explicitly an n-ary nondecomposable positive
definite Hermitian Rm-lattice ( L, h) with given discriminant 2 for every n⩾2 (resp. n⩾13 or odd n⩾3) and square-free m = 12 k + t with k⩾1 and
t∈ (1,7) (resp. k⩾1 and t = 2 or k⩾0 and t∈ 5,10,11). We study also the case for discriminant different from 2. |
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Keywords: | indecomposable lattice nondecomposable lattice dual lattice block form |
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