On the construction of indecomposable positive definite hermitian forms over imaginary quadratic fields

[摘要] Let D-m be the ring of integers of an imgainary quadratic field Q(root-m) with m = 3 (mod 4). Then there are indecomposable positive definite hermitian D-m-lattices of given rank n and given discriminant d with exactly eight exceptions if n not equal 2 and six exceptions n = 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-free m = -1 (mod 8) or m = -1 (mod 12) or the class number of Q(root-m) is unity. (C) 1997 Academic Press.

[发布日期] 1997-02-01