# Zhu reduction for Jacobi $n$-point functions and applications

## TL;DR

This paper derives Zhu reduction formulas for Jacobi n-point functions, revealing their pole structure, and applies these results to vertex operator algebras, differential operators on Jacobi forms, and Fermion models.

## Contribution

It establishes precise Zhu reduction formulas for Jacobi n-point functions and explores their implications for vertex operator algebras and Jacobi form theory.

## Key findings

- Zhu reduction formulas show no poles in Jacobi n-point functions.
- Derived new differential operators on Jacobi forms.
- Constructed Jacobi forms from Fermion model polynomials.

## Abstract

We establish precise Zhu reduction formulas for Jacobi $n$-point functions which show the absence of any possible poles arising in these formulas. We then exploit this to produce results concerning the structure of strongly regular vertex operator algebras, and also to motivate new differential operators acting on Jacobi forms. Finally, we apply the reduction formulas to the Fermion model in order to create polynomials of quasi-Jacobi forms which are Jacobi forms.