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On Dyson's crank conjecture and the uniform asymptotic behavior of certain inverse theta functions


Authors: Kathrin Bringmann and Jehanne Dousse
Journal: Trans. Amer. Math. Soc. 368 (2016), 3141-3155
MSC (2010): Primary 05A17, 11F03, 11F30, 11F50, 11P55, 11P82
DOI: https://doi.org/10.1090/tran/6409
Published electronically: November 17, 2015
MathSciNet review: 3451872
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Abstract: In this paper we prove a longstanding conjecture by Freeman Dyson concerning the limiting shape of the crank generating function. We fit this function in a more general family of inverse theta functions which play a key role in physics.


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Additional Information

Kathrin Bringmann
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: kbringma@math.uni-koeln.de

Jehanne Dousse
Affiliation: LIAFA, Universite Denis Diderot - Paris 7, 75205 Paris Cedex 13, France
Email: jehanne.dousse@liafa.univ-paris-diderot.fr

DOI: https://doi.org/10.1090/tran/6409
Received by editor(s): January 24, 2014
Received by editor(s) in revised form: February 19, 2014
Published electronically: November 17, 2015
Article copyright: © Copyright 2015 American Mathematical Society