- 作者: 余文卿
- 作者服務機構: 國立中正大學數學系
- 中文摘要: 在這論文中,我們將描述作者於1991年所創的八元數上的一階Jacobi式,然後介紹二階Jacobi式理論。透過一組theta級數的轉換式所得到的一群表現,我們建構一族Eisenstein級數,是Jacobi式的另一類典型例子。
- 英文摘要: In this paper, we outline the recent development of the theory of Jacobi forms over Cayley numbers,initiated by the author in 1991,and the theory of Jacobi forms of degree two over Cayley numbers wasdeveloped. A family of Eisenstein series is constructed via a group representation derived from thetransformation formula of a family of theta series. This provides another example of Jacobi forms besidesnatural examples from Fourier-Jacobi expansions of modular forms on the exceptional domain of 27dimensions.
- 中文關鍵字: Jacobi form; Cayley number; exceptional domain; modular form; theta series
- 英文關鍵字: --