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On a relation between certain $ q$-hypergeometric series and Maass waveforms


Authors: Matthew Krauel, Larry Rolen and Michael Woodbury
Journal: Proc. Amer. Math. Soc. 145 (2017), 543-557
MSC (2010): Primary 11F03, 11F27
DOI: https://doi.org/10.1090/proc/13246
Published electronically: August 23, 2016
MathSciNet review: 3577859
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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$.


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Additional Information

Matthew Krauel
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: mkrauel@math.uni-koeln.de

Larry Rolen
Affiliation: Department of Mathematics, 212 McAllister Building, The Pennsylvania State University, University Park, Pennsylvania 16802
Email: larryrolen@psu.edu

Michael Woodbury
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: woodbury@math.uni-koeln.de

DOI: https://doi.org/10.1090/proc/13246
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
Article copyright: © Copyright 2016 American Mathematical Society

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