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  Quantum Jacobi forms and finite evaluations of unimodal rank generating functions

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.

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http://dx.doi.org/10.1007/s00013-016-0941-z (Publisher version)
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Bringmann, Kathrin1, Author              
Folsom, Amanda1, Author              
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 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.

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Language(s): eng - English
 Dates: 2016
 Publication Status: Published in print
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 Rev. Type: Peer
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Title: Archiv der Mathematik
  Abbreviation : Arch. Math.
Source Genre: Journal
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Pages: - Volume / Issue: 107 (4) Sequence Number: - Start / End Page: 367 - 378 Identifier: -