On weak Jacobi forms of rank two

TL;DR

This paper investigates the structure of weak Jacobi forms associated with rank two lattices, providing explicit generators and a dimension formula to advance understanding of their algebraic properties.

Contribution

It introduces a finite generating set for the ring of weak Jacobi forms of rank two and derives a dimension formula, enhancing the algebraic understanding of these forms.

Findings

Explicit finite set of generators for the ring of weak Jacobi forms of rank two.

Dimension formula for weak Jacobi forms of rank two lattice index.

Structural insights into the algebraic properties of rank two weak Jacobi forms.

Abstract

We study a ring of weak Jacobi forms indexed by integral lattices of rank two. We find an explicit finite set of generators of this ring and give a dimension formula for weak Jacobi forms of rank two lattice index.