Theta type Jacobi forms
Volume 181 / 2017
Acta Arithmetica 181 (2017), 333-354
MSC: Primary 11F55, 11F50, 11E88.
DOI: 10.4064/aa161214-26-7
Published online: 24 November 2017
Abstract
Let $L$ be a positive definite even lattice. We introduce theta type Jacobi forms and construct three towers of Jacobi forms with a particularly easy pullback structure. We use theta type Jacobi forms to explain the existence of a cusp form of weight 24 with respect to the irreducible root lattice $D_{4}$ which is based on additional symmetries of the Coxeter diagram.
