On the upper bound of the orders of Jacobi forms
Abstract
In this paper, we give an upper bound of the orders of Jacobi forms. For each fixed weight , the growth rate of our upper bound divided by the index as goes to infinity is zero. Applying this result to Siegel paramodular forms, we know that the space of all formal series of Jacobi forms is finite dimensional.
Communicated by Akihiko Yukie
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