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MOC
1998

Classification of integral lattices with large class number

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Classification of integral lattices with large class number
A detailed exposition of Kneser’s neighbour method for quadratic lattices over totally real number fields, and of the sub-procedures needed for its implementation, is given. Using an actual computer program which automatically generates representatives for all isomorphism classes in one genus of rational lattices, various results about genera of -elementary lattices, for small prime level , are obtained. For instance, the class number of 12-dimensional 7-elementary even lattices of determinant 76 is 395; no extremal lattice in the sense of Quebbemann exists. The implementation incorporates as essential parts previous programs of W. Plesken and B. Souvignier.
Rudolf Scharlau, Boris Hemkemeier
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 1998
Where MOC
Authors Rudolf Scharlau, Boris Hemkemeier
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