| Summary: | 碩士 === 國立中正大學 === 應用數學研究所 === 88 === In order to construct the Maaβspace on H2 （the Hermitian upper half plane of degree two over Cayley numbers），we shall introduce the Jacobi forms on H×Cc（the product space of the upper half and Cayley numbers over the complex field C.）We shall prove that the function ψm （z,w）（m=1,2,…）appearing in the Fourier-Jacobi expansion of a modular form in the Maaβspace on H2 is a Jacobi form of weight k and index m. Furthermore, all the functionsψ0（z,w）, ψ2（z,w）, ψ3（z,w）,…are wholy determined byψ1（z,w）.
By considering the Fourier-Jacobi expansion of the modular form in the Maaβ space, we can establish an one to one correspondence between the modular forms in the Maaβ space M（k,c）and elliptic modular forms on the upper half plane of weight k-4 for positive even integer k≧4.
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