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On three theorems of Folsom, Ono and Rhoades


Author: Wadim Zudilin
Journal: Proc. Amer. Math. Soc. 143 (2015), 1471-1476
MSC (2010): Primary 11F03; Secondary 11P84, 33D15
DOI: https://doi.org/10.1090/S0002-9939-2014-12364-1
Published electronically: November 4, 2014
MathSciNet review: 3314062
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Abstract: In his deathbed letter to G.H. Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotic matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom, Ono and Rhoades have proved an elegant result about the match for a general family related to Dyson's rank (mock theta) function and the Andrews-Garvan crank (modular) function--the match with explicit formulae for implied $ O(1)$ constants. In this note we give another elementary proof of Ramanujan's original claim and outline some heuristics which may be useful for obtaining a new proof of the general Folsom-Ono-Rhoades theorem.


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Additional Information

Wadim Zudilin
Affiliation: School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan NSW 2308, Australia
Email: wadim.zudilin@newcastle.edu.au

DOI: https://doi.org/10.1090/S0002-9939-2014-12364-1
Received by editor(s): September 11, 2013
Published electronically: November 4, 2014
Additional Notes: The author was supported by the Australian Research Council.
Communicated by: Ken Ono
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.