Even positive definite unimodular quadratic forms over real quadratic fields

@article{Hsia1989EvenPD,
  title={Even positive definite unimodular quadratic forms over real quadratic fields},
  author={John S. Hsia},
  journal={Rocky Mountain Journal of Mathematics},
  year={1989},
  volume={19},
  pages={725-734}
}
  • J. Hsia
  • Published 1 September 1989
  • Mathematics
  • Rocky Mountain Journal of Mathematics
In spite of the numberous connections between even positive definite unimodular quadratic forms (henceforth referred to as even unimodular lattices) over Q with other subjects (e.g., finite group theory, geometry of numbers, combinatorial coding and design theories, automorphic functions, the explicit classification of these lattices has only been fully determined for a few cases, the most celebrated of them being undoubtedly the Leech-Niemeier-Witt [4] solution for the 24-dimensional Z… 
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7 Citations

Even positive definite unimodular quadratic forms over (√3)

A complete list of even unimodular lattices over Q(\/3) is given for each dimension n = 2, 4, 6, 8 . Siegel's mass formula is used to verify the completeness of the list. Alternate checks are given…

Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields

  • J. Hanke
  • Mathematics, Computer Science
  • 2012
TLDR
An algorithm is described that quickly computes a maximal a-valued lattice in an F-vector space equipped with a non-degenerate bilinear form, where a is a fractional ideal in a number field F.

Automorphic forms for some even unimodular lattices

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