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arXiv · 1106.4733

Modular forms of orthogonal type and Jacobi theta-series

Fabien Clery·Valery Gritsenko
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Abstract

In this paper we consider Jacobi forms of half-integral index for any positive definite lattice L (classical Jacobi forms from the book of Eichler and Zagier correspond to the lattice A_1=<2>). We give a lot of examples of Jacobi forms of singular and critical weights for root systems using Jacobi theta-series. We describe the Jacobi lifting for Jacobi forms of half-integral indices. In some case it gives additive lifting construction of new reflective modular forms.

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Fabien Clery, Valery Gritsenko. 2011-06-23. Modular forms of orthogonal type and Jacobi theta-series. https://arxiv.org/abs/1106.4733

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