engleski

On the Non-Vanishing of Certain Modular Forms

In the paper the non-vanishing of the spanning set for the space of cuspidal modular forms for Fuchsian group of the first kind of weight m, which is at least 3, is studied (the spanning set is constructed in a book of T. Miyake). The approach is based on the generalization of the non-vanishing criterion for integrable Poincare series defined for locally compact groups and proved in an earlier paper by the author. A number of very precise results is obtained in that direction.

Fuchsian group of the first kind; cuspidal modular forms; Poincare series

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