Orthogonality relations for Poincaré series
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916589173997568 |
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| author | Žunar, Sonja |
| author_facet | Žunar, Sonja |
| contents | 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 G. Muić for cusp forms on the upper half-plane, i.e., in the case when $ G=\mathrm{SL}_2(\mathbb R) $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orthogonality relations for Poincaré series Žunar, Sonja Number Theory Representation Theory 11F70, 11F46 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 G. Muić for cusp forms on the upper half-plane, i.e., in the case when $ G=\mathrm{SL}_2(\mathbb R) $. |
| title | Orthogonality relations for Poincaré series |
| topic | Number Theory Representation Theory 11F70, 11F46 |
| url | https://arxiv.org/abs/2501.17832 |