| Autor: |
Lorch, David, Kirschmer, Markus |
| Rok vydání: |
2012 |
| Předmět: |
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| Zdroj: |
LMS Journal of Computation and Mathematics / Volume 16 / 2013 / pp 172-186 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1112/S1461157013000107 |
| Popis: |
We give an enumeration of all positive definite primitive Z-lattices in dimension >= 3 whose genus consists of a single isometry class. This is achieved by using bounds obtained from the Smith-Minkowski-Siegel mass formula to computationally construct the square-free determinant lattices with this property, and then repeatedly calculating pre-images under a mapping first introduced by G. L. Watson. We hereby complete the classification of single-class genera in dimensions 4 and 5 and correct some mistakes in Watson's classifications in other dimensions. A list of all single-class primitive Z-lattices has been compiled and incorporated into the Catalogue of Lattices. |
| Databáze: |
arXiv |
| Externí odkaz: |
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