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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An arithmetic property of Fourier coefficients of singular modular forms on the exceptional domain


Authors: Shou-Te Chang and Minking Eie
Journal: Trans. Amer. Math. Soc. 353 (2001), 539-556
MSC (1991): Primary 11F55, 11F72
Published electronically: October 13, 2000
MathSciNet review: 1621733
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02371-0
PII: S 0002-9947(00)02371-0
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
Article copyright: © Copyright 2000 American Mathematical Society