## Modular forms, lattices and spherical designs.(English)Zbl 1061.11035

Martinet, Jacques (ed.), Euclidean lattices, spherical designs and modular forms. On the works of Boris Venkov. Genève: L’Enseignement Mathématique (ISBN 2-940264-02-3/pbk). Monogr. Enseign. Math. 37, 87-111 (2001).
Authors’ abstract: With the help of modular forms, we study the spherical designs which are contained in the layers of $$n$$-dimensional extremal lattices of prime level $$l$$ and determinant $$l^{4/2}$$. The method allows one to compute some Jacobi forms associated to these lattices; we derive some classifications of these extremal lattices for the levels 2, 5 and 7.
For the entire collection see [Zbl 1054.11034].

### MSC:

 11H06 Lattices and convex bodies (number-theoretic aspects) 05B05 Combinatorial aspects of block designs 11F11 Holomorphic modular forms of integral weight 11F27 Theta series; Weil representation; theta correspondences 11F50 Jacobi forms

### Keywords:

modular forms; spherical designs; Euclidean lattices