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Single-class genera of positive integral lattices

  • David Lorch (a1) and Markus Kirschmer (a1)

Abstract

We give an enumeration of all positive definite primitive $ \mathbb{Z} $ -lattices in dimension $n\geq 3$ 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 $ \mathbb{Z} $ -lattices has been compiled and incorporated into the Catalogue of Lattices.

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Copyright

© The Author(s) 2013 

References

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  • Cited by 7

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Single-class genera of positive integral lattices

  • David Lorch (a1) and Markus Kirschmer (a1)

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