Even unimodular 12-dimensional quadratic forms over Q(√5)

  title={Even unimodular 12-dimensional quadratic forms over Q(√5)},
  author={Patrick J. Costello and John S. Hsia},
  journal={Advances in Mathematics},
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
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  • 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.
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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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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
On Epstein'S zeta function of Humbert forms
The Epstein ζ function ζ(Γ,s) of a lattice Γ is defined by a series which converges for any complex number s such that ℜ s > n/2, and admits a meromorphic continuation to the complex plane, with a


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  • H. Smith
  • Mathematics
    Proceedings of the Royal Society of London
  • 1864
Let us represent by ƒ1 a homogeneous form or quantic of any order containing n indeterminates; by (α(1)), a square matrix of order n ; by (α(), its ith derived matrix, i. e. the matrix of order ∟n/∟i
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[-5, 6] promises to be the subject of many investigations. We give here a short proof that this lattice is characterised by some of its simplest properties. Although we must quote two theorems to
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