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Quantum Jacobi forms and finite evaluations of unimodal rank generating functions

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Bringmann,  Kathrin
Max Planck Institute for Mathematics, Max Planck Society;

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Folsom,  Amanda
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Bringmann, K., & Folsom, A. (2016). Quantum Jacobi forms and finite evaluations of unimodal rank generating functions. Archiv der Mathematik, 107(4), 367-378. doi:10.1007/s00013-016-0941-z.


Cite as: http://hdl.handle.net/21.11116/0000-0004-0ED9-9
Abstract
In this paper, we introduce the notion of a quantum Jacobi form, and offer the two-variable combinatorial generating function for ranks of strongly unimodal sequences as an example. We then use its quantum Jacobi properties to establish a new, simpler expression for this function as a two-variable Laurent polynomial when evaluated at pairs of rational numbers. Our results also yield a new expression for radial limits associated to the partition rank and crank functions previously studied by Ono, Rhoades, and Folsom.