THE one-dimensional Jacobi forms were first systematically investigated by Eichler and Zagier, and a similar theory in a higher-dimensional case was developed by Ziegler, who gave the precise definition and some basic properties of higher-dimensional Jacobi forms. This note tries to give a satisfactory classification for a large kind of spaces of Jacobi forms. To be a little more explicit, we get a rank formula for Jacobi forms and then show that either all the
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