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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Folsom-Ono grid contains only integers


Author: Sander Zwegers
Journal: Proc. Amer. Math. Soc. 137 (2009), 1579-1584
MSC (2000): Primary 11F11, 11F27
Published electronically: November 18, 2008
MathSciNet review: 2470815
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Abstract: In a recent paper, Folsom and Ono constructed a canonical sequence of weight 1/2 mock theta functions and a canonical sequence of weight 3/2 weakly holomorphic modular forms, both using Poincaré series. They show a remarkable symmetry in the coefficients of these functions and conjecture that all the coefficients are integers. We prove that this conjecture is true by giving an explicit construction for the weight 1/2 mock theta functions, using some results found by Guerzhoy.


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Additional Information

Sander Zwegers
Affiliation: School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Email: sander.zwegers@ucd.ie

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09684-6
PII: S 0002-9939(08)09684-6
Received by editor(s): June 30, 2008
Received by editor(s) in revised form: July 2, 2008
Published electronically: November 18, 2008
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.