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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Multiplicative $ q$-hypergeometric series arising from real quadratic fields


Authors: Kathrin Bringmann and Ben Kane
Journal: Trans. Amer. Math. Soc. 363 (2011), 2191-2209
MSC (2000): Primary 11P81, 11E16, 05A17
Published electronically: October 28, 2010
MathSciNet review: 2746680
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Abstract: Andrews, Dyson, and Hickerson showed that 2 $ q$-hypergeometric series, going back to Ramanujan, are related to real quadratic fields, which explains interesting properties of their Fourier coefficients. There is also an interesting relation of such series to automorphic forms. Here we construct more such examples arising from interesting combinatorial statistics.


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Additional Information

Kathrin Bringmann
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: kbringma@math.uni-koeln.de

Ben Kane
Affiliation: Department of Mathematics, Radboud University, Postbus 9010, 6500 GL, Nijmegen, Netherlands
Address at time of publication: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: bkane@mi.uni-koeln.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05214-6
PII: S 0002-9947(2010)05214-6
Received by editor(s): December 23, 2008
Received by editor(s) in revised form: September 27, 2009
Published electronically: October 28, 2010
Additional Notes: The first author was partially supported by NSF grant DMS-0757907 and the Alfried-Krupp prize.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.