Golden lattices

@inproceedings{Nebe2012GoldenL,
  title={Golden lattices},
  author={Gabriele Nebe},
  year={2012}
}
  • G. Nebe
  • Published 13 March 2012
  • Mathematics
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 extremal even unimodular lattices and obtain families of dense modular lattices. 
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References

SHOWING 1-10 OF 35 REFERENCES
An even unimodular 72-dimensional lattice of minimum 8
Abstract An even unimodular 72-dimensional lattice Γ having minimum 8 is constructed as a tensor product of the Barnes lattice and the Leech lattice over the ring of integers in the imaginary
Modular Lattices in Euclidean Spaces
Even lattices similar to their duals are discussed in connection with modular forms for Fricke groups. In particular, lattices of level 2 with large Hermite number are considered, and an analogy
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
Even unimodular 12-dimensional quadratic forms over Q(√5)
Dense lattices as Hermitian tensor products
Using the Hermitian tensor product description of the extremal even unimodular lattice of dimension 72 found by Nebe in 2010 we show its extremality with the methods from Coulangeons article in Acta
Lattices and Codes: A Course Partially Based on Lectures by F. Hirzebruch
Lattices and Codes - Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes
Lattices and Codes
TLDR
This section introduces the basic concept of a lattice in ℝ n and describes the construction of lattices using LaSalle's inequality.
Even positive definite unimodular quadratic forms over real quadratic fields
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
A mass formula for unimodular lattices with no roots
TLDR
A mass formula for n-dimensional unimodular lattices having any prescribed root system is derived using Katsurada's formula for the Fourier coefficients of Siegel Eisenstein series and better lower bounds are computed on the number of inequivalent unimodULAR lattices in dimensions 26 to 30 than those afforded by the Minkowski-Siegel mass constants.
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