# Modular Lattices in Euclidean Spaces

@article{Quebbemann1995ModularLI, title={Modular Lattices in Euclidean Spaces}, author={Heinz Georg Quebbemann}, journal={Journal of Number Theory}, year={1995}, volume={54}, pages={190-202} }

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 between the seven levels l such that 1 + l divides 24 is stressed.

## 111 Citations

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We investigate the relation between the vanishing order at infinity of certain cusp forms associated to integral lattices and shells of lattices being spherical t-designs. An explicit criterion is…

### On theta series attached to maximal lattices and their adjoints

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- 2009

The space spanned by theta series of adjoints of maximal even lattices of exact level $N$ and determinant $N^2$ has the Weierstrass property and hence allows to define extremality for arbitrary…

### CLASSIFICATION OF DUAL-EXTREMAL LATTICES IN LOW DIMENSIONS

- Mathematics
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In this paper we present a complete classification of dual-extremal lattices in dimensions 4 and 8, succeeded by incomplete results in higher dimensions. Furthermore we compare the notion of a…

### EXTREMAL LATTICES OF MINIMUM 8 RELATED TO THE MATHIEU GROUP M22

- Mathematics
- 1998

In this paper, we construct three new extremal lattices of minimum 8; one is 3-modular and of dimension 40, the two others are unimodular of dimension 80. They are strongly connected to the…

### Modular Forms, Lattices and Spherical Designs

- Mathematics
- 2000

With the help of modular forms, we compute some Jacobi forms associated to n-dimensional extremal lattices of prime level l and determinant l n=2. We show that the layers of these lattices support…

### Hecke actions on certain strongly modular genera of lattices

- Mathematics
- 2005

Abstract.We calculate the action of some Hecke operators on spaces of modular forms spanned by the Siegel theta-series of certain genera of strongly modular lattices closely related to the Leech…

### The Normaliser Action And Strongly Modular Lattices

- Mathematics
- 1997

We derive group theoretical methods to test if a lattice is strongly modular. We then apply these methods to the lattices of rational irreducible maximal nite groups.

### Computations of Cyclotomic Lattices

- MathematicsExp. Math.
- 1995

Even modular lattices having level l and dimension 2(p − 1) and arising from the ideal class group of the p-th cyclotomic extension of Q(√−l) are studied.