On a relation between certain $q$-hypergeometric series and Maass waveforms
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- by Matthew Krauel, Larry Rolen and Michael Woodbury PDF
- Proc. Amer. Math. Soc. 145 (2017), 543-557 Request permission
Abstract:
In this paper, we answer a question of Li, Ngo, and Rhoades concerning a set of $q$-series related to the $q$-hypergeometric series $\sigma$ from Ramanujan’s Lost Notebook. Our results parallel a theorem of Cohen which says that $\sigma$, along with its partner function $\sigma ^\star$, encode the coefficients of a Maass waveform of eigenvalue $1/4$.References
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Additional Information
- Matthew Krauel
- Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
- MR Author ID: 982089
- Email: mkrauel@math.uni-koeln.de
- Larry Rolen
- Affiliation: Department of Mathematics, 212 McAllister Building, The Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 923990
- ORCID: 0000-0001-8671-8117
- Email: larryrolen@psu.edu
- Michael Woodbury
- Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
- MR Author ID: 817209
- Email: woodbury@math.uni-koeln.de
- Received by editor(s): December 28, 2015
- Received by editor(s) in revised form: March 15, 2016, and April 12, 2016
- Published electronically: August 23, 2016
- Additional Notes: The first author was supported by the European Research Council (ERC) Grant agreement n. 335220 - AQSER
The second author thanks the University of Cologne and the DFG for their generous support via the University of Cologne postdoc grant DFG Grant D-72133-G-403-151001011, funded under the Institutional Strategy of the University of Cologne within the German Excellence Initiative - Communicated by: Kathrin Bringmann
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 543-557
- MSC (2010): Primary 11F03, 11F27
- DOI: https://doi.org/10.1090/proc/13246
- MathSciNet review: 3577859