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].


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