A short proof of the Mock Theta Conjectures using Maass forms
Author:
Amanda Folsom
Journal:
Proc. Amer. Math. Soc. 136 (2008), 41434149
MSC (2000):
Primary 11F37
Published electronically:
June 17, 2008
MathSciNet review:
2431026
Fulltext PDF Free Access
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Additional Information
Abstract: A celebrated work of D. Hickerson gives a proof of the Mock Theta Conjectures using Hecketype identities discovered by G. Andrews. Here, we respond to a remark by K. Bringmann, K. Ono and R. Rhoades and provide a short proof of the Mock Theta Conjectures by realizing each side of the identities as the holomorphic projection of a harmonic weak Maass form.
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 K. Bringmann and K. Ono, The mock theta function conjecture and partition ranks, Inventiones Math. 165 (2006), 243266. MR 2231957 (2007e:11127)
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 K. Bringmann, K. Ono, and R. Rhoades, Eulerian series as modular forms, Journal of the Amer. Math. Soc., accepted for publication.
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 K. Bringmann, Asymptotics for rank partition functions, Trans. Amer. Math. Soc., accepted for publication.
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 S. P. Zwegers, Mock theta functions, Ph.D. Thesis, Universiteit Utrecht (2002).
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Additional Information
Amanda Folsom
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
Email:
folsom@math.wisc.edu
DOI:
http://dx.doi.org/10.1090/S0002993908094343
PII:
S 00029939(08)094343
Received by editor(s):
November 5, 2007
Published electronically:
June 17, 2008
Additional Notes:
The author is grateful for a National Science Foundation Postdoctoral Fellowship and wishes to thank Ken Ono for suggesting this project. The author also thanks the referee for a very detailed and thoughtful report, including useful suggestions that have helped ease the exposition of this paper.
Communicated by:
Ken Ono
Article copyright:
© Copyright 2008 American Mathematical Society
