Jacobi Forms of Indefinite Lattice Index

TL;DR

This paper introduces Jacobi forms associated with indefinite lattices, establishes their isomorphism with vector-valued modular forms, and explores operations and bilinear maps connecting these mathematical objects.

Contribution

It defines Jacobi forms of indefinite lattice index and proves their isomorphism with vector-valued modular forms, expanding the understanding of their structure and interactions.

Findings

Jacobi forms of indefinite lattice index are isomorphic to vector-valued modular forms.

Operations on these forms lead to a bilinear map between vector-valued modular forms.

The work broadens the framework for studying modular forms related to indefinite lattices.

Abstract

We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of the two types of objects, and obtain an interesting bilinear map between vector-valued modular forms arising from the product operation.