On the Restriction Map for Jacobi Forms

TL;DR

This paper characterizes the kernel of the restriction map for Jacobi forms of index 2 and proves injectivity of specific differential operators, extending results to certain subspaces with square-free index.

Contribution

It provides a detailed description of the restriction map kernel for Jacobi forms of index 2 and generalizes these results to subspaces with square-free index m.

Findings

Kernel of the restriction map for Jacobi forms of index 2 described.

Injectivity of D_0 ⊕ D_2 on weight 2, index 2 Jacobi forms established.

Results extended to subspaces with square-free index m.

Abstract

In this article we give the description of the kernel of the restriction map for Jacobi forms of index 2 and obtain the injectivity of $D_0\oplus D_2$ on the space of Jacobi forms of weight 2 and index 2. We also obtain certain generalization of these results on certain subspace of Jacobi forms of square-free index $m$.