摘要
Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of integers Rm of an imaginary quadratic field ?(√?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.
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=12k+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.
