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… 
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
Automorphic forms for some even unimodular lattices
We look at genera of even unimodular lattices of rank 12 over the ring of integers of $${{\mathbb {Q}}}(\sqrt{5})$$ Q ( 5 ) and of rank 8 over the ring of integers of $${{\mathbb {Q}}}(\sqrt{3})$$ Q
Golden lattices
Let θ := −1+ √ 5 2 be the golden ratio. A golden lattice is an even unimodular Z[θ]-lattice of which the Hilbert theta series is an extremal Hilbert modular form. We construct golden lattices from

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