On certain explicit congruences for mock theta functions
Author:
Matthias Waldherr
Journal:
Proc. Amer. Math. Soc. 139 (2011), 865879
MSC (2010):
Primary 11F33, 11F37
Published electronically:
August 19, 2010
MathSciNet review:
2745639
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Abstract 
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Additional Information
Abstract: Recently, Garthwaite and Penniston have shown that the coefficients of Ramanujan's mock theta function satisfy infinitely many congruences of Ramanujan type. In this work we give the first explicit examples of congruences for Ramanujan's mock theta function and another mock theta function .
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Dyson's crank of a partition. Bull. Amer. Math. Soc., New Ser., 18(2):167171, 1988. MR 929094 (89b:11079)
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On the theorems of Watson and Dragonette for Ramanujan's mock theta functions. Amer. J. Math., 88:454490, 1966. MR 0200258 (34:157)
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 J. Bruinier and J. Funke.
On two geometric theta lifts. Duke Math. J., 125(1):4590, 2004. MR 2097357 (2005m:11089)
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 K. Bringmann and K. Ono.
The mock theta function conjecture and partition ranks. Invent. Math., 165(2):243266, 2006. MR 2231957 (2007e:11127)
 [BO08]
 J. Bruinier and K. Ono.
Identities and congruences for the coefficients of Ramanujan's . Special issue of the Ramanujan Journal in celebration of G. E. Andrews's th Birthday, 2008.
 [BO10]
 K. Bringmann and K. Ono.
Dyson's rank and Maass forms. Ann. of Math. (2), 171:419449, 2010.
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 K. Bringmann.
Asymptotics for rank partition functions. Trans. Amer. Math. Soc., 361(7):34833500, 2009. MR 2491889
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 S. Chan.
Congruences for Ramanujan's function. Preprint, 2010.
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 L. Dragonette.
Some asymptotic formulae for the mock theta series of Ramanujan. Trans. Amer. Math. Soc., 72:474500, 1952. MR 0049927 (14:248g)
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 F. Dyson.
Some guesses in the theory of partitions. Eureka, 8:1015, 1944.
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The coefficients of the Mock theta function. Int. J. Number Theory, 4(6):10271042, 2008. MR 2483310
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adic properties of Maass forms arising from theta series. Math. Res. Lett., 15(23):459470, 2008. MR 2407223 (2009f:11049)
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Partition congruences and the AndrewsGarvanDyson crank. Proc. Natl. Acad. Sci. USA, 102(43):1537315376, 2005. MR 2188922 (2006k:11200)
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Mock Theta Functions. Ph.D. thesis, July 2002. Comments: Ph.D. thesis, Utrecht University, 2002. With Dutch title page and abstract.
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Additional Information
Matthias Waldherr
Affiliation:
Mathematical Institute, University of Cologne, Weyertal 8690, 50931 Cologne, Germany
Email:
mwaldher@math.unikoeln.de
DOI:
http://dx.doi.org/10.1090/S000299392010105385
Received by editor(s):
March 25, 2010
Received by editor(s) in revised form:
April 14, 2010
Published electronically:
August 19, 2010
Additional Notes:
The author is supported by Graduiertenkolleg “Global Structures in Geometry and Analysis”
Communicated by:
Kathrin Bringmann
Article copyright:
© Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
