On the non-vanishing of Poincaré series on irreducible bounded symmetric domains
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910781875945472 |
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| author | Žunar, Sonja |
| author_facet | Žunar, Sonja |
| contents | Let $ \mathcal D\equiv G/K $ be an irreducible bounded symmetric domain. Using a vector-valued version of Muić's integral non-vanishing criterion for Poincaré series on locally compact Hausdorff groups, we study the non-vanishing of holomorphic automorphic forms on $ \mathcal D $ that are given by Poincaré series of polynomial type and correspond via the classical lift to the Poincaré series of certain $ K $-finite matrix coefficients of integrable discrete series representations of $ G $. We provide an example application of our results in the case when $ G=\mathrm{SU}(p,q) $ and $ K=\mathrm S(\mathrm U(p)\times\mathrm U(q)) $ with $ p\geq q\geq1 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the non-vanishing of Poincaré series on irreducible bounded symmetric domains Žunar, Sonja Number Theory Representation Theory 11F55, 11F70, 22E46 Let $ \mathcal D\equiv G/K $ be an irreducible bounded symmetric domain. Using a vector-valued version of Muić's integral non-vanishing criterion for Poincaré series on locally compact Hausdorff groups, we study the non-vanishing of holomorphic automorphic forms on $ \mathcal D $ that are given by Poincaré series of polynomial type and correspond via the classical lift to the Poincaré series of certain $ K $-finite matrix coefficients of integrable discrete series representations of $ G $. We provide an example application of our results in the case when $ G=\mathrm{SU}(p,q) $ and $ K=\mathrm S(\mathrm U(p)\times\mathrm U(q)) $ with $ p\geq q\geq1 $. |
| title | On the non-vanishing of Poincaré series on irreducible bounded symmetric domains |
| topic | Number Theory Representation Theory 11F55, 11F70, 22E46 |
| url | https://arxiv.org/abs/2501.06876 |