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Zbl 0936.68129
Schiemann, Alexander
Classification of Hermitian forms with the neighbour method. (English)
[J] J. Symb. Comput. 26, No. 4, 487-508 (1998). ISSN 0747-7171

Summary: The neighbour method of Kneser can be adapted to the Hermitian case. Generalizing results of {\it D. W. Hoffmann} [Manuscr. Math. 71, No. 4, 399--429 (1991; Zbl 0729.11020)], we show that it can be used to classify any genus in a Hermitian space of dimension $\geq 2$ by neighbour steps at suitable primes. The method was implemented for positive definite Hermitian lattices (not necessarily free) over $\Bbb Q(\sqrt d)$. 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.

MSC 2000:: *11E41 Class numbers of quadratic and Hermitian forms
11H50 Minima of forms
11H55 Quadratic forms
11Y16 Algorithms

Keywords: neighbour method of Kneser; LLL-algorithm

Citations: Zbl 0729.11020

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Zentralblatt MATH Berlin [Germany]