On the classification of positive definite unimodular Hermitian forms
The author studies the problem of classification of positive definite unimodular Hermitian forms over the ring of integers \(D_ m\) of imaginary quadratic fields \(\mathbb{Q}(\sqrt{-m})\) with class number one (i.e., \(m=1,2,3,7,11,19,43,67,163)\). Using Hermitian reduction theory to such Hermitian forms he finds the class numbers \(C_{n,m}\) and \(C_{n,m}'\) (resp. \(h_{n,m}\) and \(h_{n,m}'\), the special unitary class numbers) of odd and even genus of \(n\)-ary positive defnite unimodular Hermitian forms over \(D_ m\) respectively. Representatives of each class are exhibited. For the proofs of these results, see the author's papers [Northeastern Math. J. 6, No. 3, 327-338 (1990; Zbl 0741.11021); J. Math., Wuhan Univ. 11, No. 2, 188-195 (1991; Zbl 0753.11019); Chin. Ann. Math., Ser. A 12, No. 6, 720-730 (in Chinese) (1991; see below); Northeastern Math. J. 9, No. 1, 89-97 (1993)].
scientific article; zbMATH DE number 62526