Eulerian series as modular forms
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- by Kathrin Bringmann, Ken Ono and Robert C. Rhoades
- J. Amer. Math. Soc. 21 (2008), 1085-1104
- DOI: https://doi.org/10.1090/S0894-0347-07-00587-5
- Published electronically: November 26, 2007
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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.References
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Bibliographic Information
- Kathrin Bringmann
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 774752
- Email: bringman@math.umn.edu
- Ken Ono
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- MR Author ID: 342109
- Email: ono@math.wisc.edu
- Robert C. Rhoades
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- MR Author ID: 762187
- Email: rhoades@math.wisc.edu
- 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.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 21 (2008), 1085-1104
- MSC (2000): Primary 11P99, 11F11, 05A19
- DOI: https://doi.org/10.1090/S0894-0347-07-00587-5
- MathSciNet review: 2425181