# 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}
}
18 Citations

### Span of Restriction of Hilbert Theta Functions

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• 2022
. 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

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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
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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

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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

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

• J. Hanke
• Mathematics, Computer Science
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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

## 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