On nondecomposable positive definite Hermitian forms over imaginary quadratic fields

Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of integers R-m of an imaginary quadratic field Q( (root)-m). Using our methods, one can construct explicitly an n-ary nondecomposable positive definite Hermitian R-m-lattice ( L, h) with given discriminant 2 for every n greater than or equal to2 (resp. n greater than or equal to 13 or odd n greater than or equal to3) and square-free m = 12k + t with k greater than or equal tol and t is an element ofE {1,7} (resp. k greater than or equal tol and t=2 or k greater than or equal to0 and t is an element of {5,10,11}). We study also the case for discriminant different from 2.