Multivariable Appell functions and nonholomorphic Jacobi forms

  • Sander ZwegersEmail author


Multivariable Appell functions show up in the work of Kac and Wakimoto in the computation of character formulas for certain \(s \ell (m,1)^\wedge \) modules. Bringmann and Ono showed that the character formulas for the \(s \ell (m,1)^\wedge \) modules \(L(\varLambda _{(s)})\), where \(L(\varLambda _{(s)})\) is the irreducible \(s \ell (m,1)^\wedge \) module with the highest weight \(\varLambda _{(s)}\), can be seen as the “holomorphic parts” of certain nonholomorphic modular functions. Here, we consider more general multivariable Appell functions and relate them to nonholomorphic Jacobi forms.


Appell functions Jacobi forms Mock modular forms Nonholomorphic modular forms 

Mathematics Subject Classification

11F27 11F30 11F50 



The author wishes to thank Kathrin Bringmann and the referees for their comments.


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Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of CologneCologneGermany

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