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The Folsom-Ono grid contains only integers

Author(s): Sander Zwegers
Journal: Proc. Amer. Math. Soc. 137 (2009), 1579-1584.
MSC (2000): Primary 11F11, 11F27
Posted: November 18, 2008
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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.

References:

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K. Bringmann and K. Ono, The $ f(q)$ mock theta function conjecture and partition ranks, Invent. Math. 165 (2006), pp. 243-266. MR 2231957 (2007e:11127)

2.
A. Folsom and K. Ono, Duality involving the mock theta function $ f(q)$, J. London Math. Soc. 77 (2008), pp. 320-334. MR 2400394

3.
-, Corrigendum: Duality involving the mock theta function $ f(q)$, J. London Math. Soc., to appear.

4.
P. Guerzhoy, Rationality of the Folsom-Ono grid, Proc. Amer. Math. Soc., accepted for publication.

5.
D. Mumford, Tata Lectures on Theta. I, Progress in Mathematics, no. 28, Birkhäuser Boston, 1983. MR 688651 (85h:14026)

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PARI/GP, version 2.3.1, Bordeaux, 2006, http://pari.math.u-bordeaux.fr/.

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S. P. Zwegers, Mock $ \theta$-functions and real analytic modular forms, $ q$-Series with Applications to Combinatorics, Number Theory, and Physics, Contemporary Mathematics, vol. 291, Amer. Math. Soc., 2001, pp. 269-277. MR 1874536 (2003f:11061)

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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: 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
Posted: November 18, 2008
Communicated by: Ken Ono
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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