An arithmetic property of Fourier coefficients of singular modular forms on the exceptional domain
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- by Shou-Te Chang and Minking Eie PDF
- Trans. Amer. Math. Soc. 353 (2001), 539-556 Request permission
Abstract:
We shall develop the theory of Jacobi forms of degree two over Cayley numbers and use it to construct a singular modular form of weight 4 on the 27-dimensional exceptional domain. Such a singular modular form was obtained by Kim through the analytic continuation of a nonholomorphic Eisenstein series. By applying the results in a joint work with Eie, A. Krieg provided an alternative proof that a function with a Fourier expansion obtained by Kim is indeed a modular form of weight 4. This work provides a systematic and general approach to deal with the whole issue.References
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Additional Information
- Shou-Te Chang
- Affiliation: Department of Mathematics, National Chung Cheng University, Min-Hsiung Chiayi 621, Taiwan
- Email: stchang@math.ccu.edu.tw
- Minking Eie
- Affiliation: Department of Mathematics, National Chung Cheng University, Min-Hsiung Chiayi 621, Taiwan
- Email: eie@math.ccu.edu.tw
- Received by editor(s): March 14, 1997
- Received by editor(s) in revised form: October 28, 1997, January 27, 1998, and April 1, 1998
- Published electronically: October 13, 2000
- Additional Notes: This work was supported by the Department of Mathematics, National Chung Cheng University, and by the National Science Foundation of Taiwan, Republic of China
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 539-556
- MSC (1991): Primary 11F55, 11F72
- DOI: https://doi.org/10.1090/S0002-9947-00-02371-0
- MathSciNet review: 1621733