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Classification of Hermitian Forms with the Neighbour Method

โœ Scribed by A Schiemann

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
698 KB
Volume
26
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

The neighbour method of Kneser can be adapted to the hermitian case. Generalizing results of Hoffmann (1991), we show that it can be used to classify any genus in a hermitian space of dimension โ‰ฅ2 by neighbour steps at suitable primes. The method was implemented for positive definite hermitian lattices (not necessarily free) over Q ( โˆš 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.

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