Hecke Bound of Vector-valued Modular Forms and its Relationship with Cuspidality

초록

In this paper, we prove that if the Fourier coefficients of a vector-valued modular form satisfy the Hecke bound, then it is cuspidal. Furthermore, we obtain an analogous result with regard to Jacobi forms by applying an isomorphism between vector-valued modular forms and Jacobi forms. As an application, we prove a result on the growth of the number of representations of m by a positive definite quadratic form Q.

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