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We establish precise Zhu reduction formulas for Jacobi $n$-point functionswhich show the absence of any possible poles arising in these formulas. We thenexploit this to produce results concerning the structure of strongly regularvertex operator algebras, and also to motivate new differential operatorsacting on Jacobi forms. Finally, we apply the reduction formulas to the Fermionmodel in order to create polynomials of quasi-Jacobi forms which are Jacobiforms.

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