Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras
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- by Henry H. Kim, Kyu-Hwan Lee and Yichao Zhang PDF
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Abstract:
In this paper, we compute basis elements of certain spaces of weight $0$ weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. We use the results to construct automorphic correction of the rank $2$ hyperbolic Kac-Moody algebras $\mathcal H(a)$, $a=4,5,6$, through Hilbert modular forms explicitly given by Borcherds lifts of the weakly holomorphic modular forms. We also compute asymptotics of the Fourier coefficients as they are related to root multiplicities of the rank $2$ hyperbolic Kac-Moody algebras. This work is a continuation of an earlier work of the first and second authors, where automorphic correction was constructed for $\mathcal H(a)$, $a=3, 11, 66$.References
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Additional Information
- Henry H. Kim
- Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada – and – Korea Institute for Advanced Study, Seoul, Korea
- MR Author ID: 324906
- Email: henrykim@math.toronto.edu
- Kyu-Hwan Lee
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- MR Author ID: 650497
- Email: khlee@math.uconn.edu
- Yichao Zhang
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- Address at time of publication: Department of Mathematics, The University of Arizona, Tucson, Arizona 85721
- MR Author ID: 881604
- Email: yichao.zhang@uconn.edu, yichaozhang@math.arizona.edu
- Received by editor(s): September 19, 2013
- Received by editor(s) in revised form: January 21, 2014, and April 2, 2014
- Published electronically: March 13, 2015
- Additional Notes: The first author was partially supported by an NSERC grant.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 367 (2015), 8843-8860
- MSC (2010): Primary 11F22; Secondary 17B67, 11F41
- DOI: https://doi.org/10.1090/S0002-9947-2015-06438-1
- MathSciNet review: 3403073