10 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.
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…
Extremal Lattices
- MathematicsAlgorithmic Algebra and Number Theory
- 1997
This paper deals with discrete subgroups of euclidean vector spaces, equivalently finitely generated free abelian groups (isomorphic to Z for some n ∈ N) together with a positive definite quadratic…
On the genera and the class number of unimodular lattices over the ring of integers in real quadratic fields
- Mathematics
- 1990
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…
On Epstein'S zeta function of Humbert forms
- Mathematics
- 2008
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…
References
SHOWING 1-10 OF 38 REFERENCES
Automorphism groups of 24-dimensional even unimodular lattices
- Mathematics
- 1984
A description of the automorphism groups of even positive-definite unimodular 24-dimensional lattices is given.
Einklassige Geschlechter totalpositiver quadratischer Formen in totalreellen algebraischen Zahlkörpern
- Mathematics
- 1971
Some properties of Fourier coefficients of Eisenstein series of degree two.
- Mathematics
- 1974
§1. The Fourier coefficients of those elliptic modular forms which are eigenfunctions of the ring of Hecke operators possess remarkable multiplicative properties which permit the representation of…
Symmetric Bilinear Forms
- Mathematics
- 1973
I. Basic Concepts.- II. Symmetric Inner Product Spaces over Z.- III. Inner Product Spaces over a Field.- IV. Discrete Valuations and Dedekind Domains.- V. Some Examples.- Appendix 1. Quadratic…
On the orders and genera of quadratic forms containing more than three indeterminates
- MathematicsProceedings 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…
A characterisation of Leech's lattice
- Mathematics
- 1969
[-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…
Introduction to quadratic forms
- Mathematics
- 1963
Prerequisites ad Notation Part One: Arithmetic Theory of Fields I Valuated Fields Valuations Archimedean Valuations Non-Archimedean valuations Prolongation of a complete valuation to a finite…