The Folsom-Ono grid contains only integers
Author:
Sander Zwegers
Journal:
Proc. Amer. Math. Soc. 137 (2009), 1579-1584
MSC (2000):
Primary 11F11, 11F27
DOI:
https://doi.org/10.1090/S0002-9939-08-09684-6
Published electronically:
November 18, 2008
MathSciNet review:
2470815
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- 1. Kathrin Bringmann and Ken Ono, The 𝑓(𝑞) mock theta function conjecture and partition ranks, Invent. Math. 165 (2006), no. 2, 243–266. MR 2231957, https://doi.org/10.1007/s00222-005-0493-5
- 2. Amanda Folsom and Ken Ono, Duality involving the mock theta function 𝑓(𝑞), J. Lond. Math. Soc. (2) 77 (2008), no. 2, 320–334. MR 2400394, https://doi.org/10.1112/jlms/jdm119
- 3.
-, Corrigendum: Duality involving the mock theta function
, J. London Math. Soc., to appear.
- 4. P. Guerzhoy, Rationality of the Folsom-Ono grid, Proc. Amer. Math. Soc., accepted for publication.
- 5. David Mumford, Tata lectures on theta. I, Progress in Mathematics, vol. 28, Birkhäuser Boston, Inc., Boston, MA, 1983. With the assistance of C. Musili, M. Nori, E. Previato and M. Stillman. MR 688651
- 6. PARI/GP, version 2.3.1, Bordeaux, 2006, http://pari.math.u-bordeaux.fr/.
- 7. S. P. Zwegers, Mock 𝜃-functions and real analytic modular forms, 𝑞-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000) Contemp. Math., vol. 291, Amer. Math. Soc., Providence, RI, 2001, pp. 269–277. MR 1874536, https://doi.org/10.1090/conm/291/04907
mock theta function conjecture and partition ranks, Invent. Math. 165 (2006), pp. 243-266. 
, J. London Math. Soc. 77 (2008), pp. 320-334. 
-functions and real analytic modular forms, 
-Series with Applications to Combinatorics, Number Theory, and Physics, Contemporary Mathematics, vol. 291, Amer. Math. Soc., 2001, pp. 269-277. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F11, 11F27
Retrieve articles in all journals with MSC (2000): 11F11, 11F27
Additional Information
Sander Zwegers
Affiliation:
School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Email:
sander.zwegers@ucd.ie
DOI:
https://doi.org/10.1090/S0002-9939-08-09684-6
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.
