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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Eulerian series as modular forms


Authors: Kathrin Bringmann, Ken Ono and Robert C. Rhoades
Journal: J. Amer. Math. Soc. 21 (2008), 1085-1104
MSC (2000): Primary 11P99, 11F11, 05A19
Published electronically: November 26, 2007
MathSciNet review: 2425181
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Abstract: In 1988, Hickerson proved the celebrated ``mock theta conjectures'' in a collection of ten identities from Ramanujan's ``lost notebook'' which express certain modular forms as linear combinations of mock theta functions. In the context of Maass forms, these identities arise from the peculiar phenomenon that two different harmonic Maass forms may have the same non-holomorphic parts. Using this perspective, we construct several infinite families of modular forms which are differences of mock theta functions.


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Additional Information

Kathrin Bringmann
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: bringman@math.umn.edu

Ken Ono
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: ono@math.wisc.edu

Robert C. Rhoades
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: rhoades@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-07-00587-5
PII: S 0894-0347(07)00587-5
Keywords: Mock theta functions, Maass forms
Received by editor(s): March 28, 2007
Published electronically: November 26, 2007
Additional Notes: The authors thank the National Science Foundation for its support. The third author is supported by an NSF Graduate Fellowship and a National Physical Science Consortium Graduate Fellowship.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.