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An arithmetic property of Fourier coefficients of singular modular forms on the exceptional domain
Author(s):
Shou-Te
Chang;
Minking
Eie
Journal:
Trans. Amer. Math. Soc.
353
(2001),
539-556.
MSC (1991):
Primary 11F55, 11F72
Posted:
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:
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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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