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arXiv · 1208.5638

Single-Class Genera of Positive Integral Lattices

David Lorch·Markus Kirschmer
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Abstract

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.

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David Lorch, Markus Kirschmer. 2013-05-14. Single-Class Genera of Positive Integral Lattices. https://doi.org/10.1112/s1461157013000107

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