Classification of Hermitian Forms with the Neighbour Method
Classification of Hermitian Forms with the Neighbour Method
复制标题
用邻域法对埃尔米特形式进行分类
DOI：
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发表时间：
1998
影响因子：
0.7
通讯作者：
A. Schiemann
中科院分区：
文献类型：
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作者：
A. Schiemann
Kneser的近邻法可适用于埃尔米特的情况。推广了Hoffmann（1991）的结果，证明了它可以用于维？2在适当的素数上通过相邻步骤。该方法实现了正定埃尔米特格（不一定是自由的）在Q（d 1/2）。给出了么模属的类数表和在这些属中获得的最大极小值。我们还描述了一个推广的LLL算法的格在正厄米空间的数域。
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 ?2 by neighbour steps at suitable primes. The method was implemented for positive definite hermitian lattices (not necessarily free) over Q(d1/2). 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.