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

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**, 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**, 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**, 10.1090/conm/291/04907

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.