Unimodular lattices over real quadratic fields

@article{Scharlau1994UnimodularLO,
  title={Unimodular lattices over real quadratic fields},
  author={Rudolf Scharlau},
  journal={Mathematische Zeitschrift},
  year={1994},
  volume={216},
  pages={437-452}
}

Span of Restriction of Hilbert Theta Functions

. In this paper, we study the diagonal restrictions of certain Hilbert theta series for a totally real field F , and prove that they span the corresponding space of elliptic modular forms when the F

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

Coincidence rotations of the root lattice A 4 Journal Item

The coincidence site lattices of the root lattice A4 are considered, and the statistics of the corresponding coincidence rotations according to their indices is expressed in terms of a Dirichlet

One Class Genera of Lattice Chains Over Number Fields

We classify all one-class genera of admissible lattice chains of length at least 2 in hermitian spaces over number fields. If L is a lattice in the chain and \(\mathfrak {p} \) the prime ideal

One-class genera of maximal integral quadratic forms

Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields

  • J. Hanke
  • Mathematics, Computer Science
  • 2012
TLDR
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.

Regularized theta lifts for orthogonal groups over totally real fields

Abstract We define a regularized theta lift from SL2 to orthogonal groups over totally real fields. It takes harmonic ‘Whittaker forms’ to automorphic Green functions and weakly holomorphic Whittaker

Coincidence rotations of the root lattice A4

References

SHOWING 1-10 OF 26 REFERENCES

Groupes et algèbres de Lie

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements. Ce premier volume du Livre sur

Positive Definite Unimodular Lattices with Trivial Automorphism Groups

The disclosed signal multiplexing circuit makes use of a single pair of wires to interface a data and voice communication circuit such as an electronic key telephone (EKT) station set with a central

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

Introduction to quadratic forms

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