Orthogonality relations for Poincaré series.
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| Title: | Orthogonality relations for Poincaré series. |
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| Authors: | Žunar, Sonja1 szunar@geof.hr |
| Source: | Mathematical Communications. 2025, Vol. 30 Issue 2, p161-169. 9p. |
| Subjects: | Poincaré series, Automorphic forms, Lie groups, Inner product spaces |
| Abstract: | Let G be a connected semisimple Lie group with finite center. We prove a formula for the inner product of two cuspidal automorphic forms on G that are given by Poincaré series of K-finite matrix coefficients of an integrable discrete series representation of G. As an application, we give a new proof of a well-known result on the Petersson inner product of certain vector-valued Siegel cusp forms. In this way, we extend results previously obtained by Muić for cusp forms on the upper half-plane, i.e., in the case when G = SL2 (R). [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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