# 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} }

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…

## 7 Citations

### Even positive definite unimodular quadratic forms over (√3)

- Mathematics
- 1991

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

- Mathematics, Computer Science
- 2012

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

- MathematicsAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg
- 2021

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

- Mathematics
- 2012

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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