On a relation between certain 
-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 | References | Similar Articles | Additional Information
Abstract: In this paper, we answer a question of Li, Ngo, and Rhoades concerning a set of 
-series related to the 
-hypergeometric series 
from Ramanujan's Lost Notebook. Our results parallel a theorem of Cohen which says that 
, along with its partner function 
, encode the coefficients of a Maass waveform of eigenvalue 
.
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-hypergeometric series arising from real quadratic fields, Trans. Amer. Math. Soc. 363 (2011), no. 4, 2191-2209. 
-identities for Maass waveforms, Invent. Math. 91 (1988), no. 3, 409-422. 
-series in 
, J. Number Theory 107 (2004), no. 2, 392-405. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11F03, 11F27
Retrieve articles in all journals with MSC (2010): 11F03, 11F27
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
