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Spectral Decomposition of Compactly Supported Poincare Series and Existence of Cusp Forms

In the paper, the issue of existence of cusp forms is addressed, using an extension and refinement of a classical method of (adelic) compactly supported Poincare series. The cusp forms for congruence subgroups are considered also, as a consequence of the adelic approach which is used in the paper.

semisimple group; number field; adeles; cusp forms; Poincare series

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