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On identities involving the sixth order mock theta functions
Author(s):
Jeremy
Lovejoy
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2547-2552.
MSC (2010):
Primary 33D15
Posted:
March 3, 2010
MathSciNet review:
2607884
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Abstract:
We present  -series proofs of four identities involving sixth order mock theta functions from Ramanujan's lost notebook. We also show how Ramanujan's identities can be used to give a quick proof of four sixth order identities of Berndt and Chan.
References:
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- 1.
- G.E. Andrews, On basic hypergeometric series, mock theta functions, and partitions. I, Quart. J. Math. 17 (1966), 64-80. MR 0193282 (33:1502)
- 2.
- G.E. Andrews and B.C. Berndt, Ramanujan's Lost Notebook. Part II, Springer, New York, 2009. MR 2474043
- 3.
- G.E. Andrews and D. Hickerson, Ramanujan's ``lost'' notebook. VII: The sixth order mock theta functions, Adv. Math. 89 (1991), 60-105. MR 1123099 (92i:11027)
- 4.
- B.C. Berndt and S.H. Chan, Sixth order mock theta functions, Adv. Math. 216 (2007), 771-786. MR 2351377 (2008i:33046)
- 5.
- J.M. Borwein, P.B. Borwein, and F.G. Garvan, Cubic modular identities of Ramanujan, Trans. Amer. Math. Soc. 343 (1994), 35-47. MR 1243610 (94j:11019)
- 6.
- G. Gasper and M. Rahman, Basic Hypergeometric Series,
 nd Ed., Cambridge Univ. Press, Cambridge, 2004. MR 2128719 (2006d:33028) - 7.
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- 8.
- K. Ono, The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and
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- S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988. MR 947735 (89j:01078)
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Additional Information:
Jeremy
Lovejoy
Affiliation:
Laboratorie d'Informatique Algorithmique: Fondements et Applications, CNRS UMR 7089, Université Denis Diderot - Paris 7, Case 7014, 75205 Paris Cedex 13, France
Email:
lovejoy@liafa.jussieu.fr
DOI:
10.1090/S0002-9939-10-10296-2
PII:
S 0002-9939(10)10296-2
Received by editor(s):
November 19, 2009
Posted:
March 3, 2010
Communicated by:
Ken Ono
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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