Jacobi Forms of Degree One and Weil Representations

TL;DR

This paper explores Jacobi forms of degree one with matrix index, providing dimension formulas, examples, and connections to Weil representation invariants, advancing understanding in modular form theory.

Contribution

It introduces the notion of Jacobi forms of degree one with matrix index and links their theory to Weil representation invariants, offering new insights and explicit formulas.

Findings

Dimension formulas for Jacobi forms of degree one

Explicit examples illustrating the theory

Connection established between Jacobi forms and Weil invariants

Abstract

We discuss the notion of Jacobi forms of degree one with matrix index, we state dimension formulas, give explicit examples, and indicate how closely their theory is connected to the theory of invariants of Weil representations associated to finite quadratic modules.