On the Construction of Indecomposable Positive Definite Hermitian Forms over Imaginary Quadratic Fields Original Research Article

LetDmbe the ring of integers of an imgainary quadratic fieldimagewithm≡3 (mod 4). Then there are indecomposable positive definite hermitianDm-lattices of given ranknand given discriminantdwith exactly eight exceptions ifn≠2 and six exceptions ifn=2 and assume the generalized Riemann hypothesis. In these exceptional cases there are no lattices with the desired properties. In particular, this result holds without assuming the generalized Riemann hypothesis, if the square-freem≡−1 (mod 8) orm≡−1 (mod 12) or the class number ofimageis unity.