CLASSIFICATION OF HERMITIAN-FORMS WITH THE NEIGHBOR METHOD

The neighbour method of Kneser can be adapted to the hermitian case. G eneralizing results of Hoffmann (1991), we show that it can be used to classify any genus in a hermitian space of dimension greater than or equal to 2 by neighbour steps at suitable primes. The method was imple mented for positive definite hermitian lattices (not necessarily free) over Q(root d). A table of class numbers of unimodular genera and the largest minima attained in those genera is given. We also describe a generalization of the LLL-algorithm to lattices in positive hermitian spaces over number fields. (C) 1998 Academic Press.