Multiplicative $q$-hypergeometric series arising from real quadratic fields
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- by Kathrin Bringmann and Ben Kane
- Trans. Amer. Math. Soc. 363 (2011), 2191-2209
- DOI: https://doi.org/10.1090/S0002-9947-2010-05214-6
- Published electronically: October 28, 2010
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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.References
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Bibliographic Information
- Kathrin Bringmann
- Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
- MR Author ID: 774752
- 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
- MR Author ID: 789505
- Email: bkane@mi.uni-koeln.de
- 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.
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 2191-2209
- MSC (2000): Primary 11P81, 11E16, 05A17
- DOI: https://doi.org/10.1090/S0002-9947-2010-05214-6
- MathSciNet review: 2746680