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

DOI:
https://doi.org/10.1090/S0894-0347-07-00587-5

Published electronically:
November 26, 2007

MathSciNet review:
2425181

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0894-0347-07-00587-5

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.