On vector-valued automorphic forms on bounded symmetric domains
| Autor: | Alluhaibi, Nadia, Barron, Tatyana |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove a spanning result for vector-valued Poincar\'e series on a bounded symmetric domain. We associate a sequence of holomorphic automorphic forms to a submanifold of the domain. When the domain is the unit ball in ${\Bbb{C}}^n$, we provide estimates for the norms of these automorphic forms and we find asymptotics of the norms (as the weight goes to infinity) for a class of totally real submanifolds. We give an example of a CR submanifold of the ball, for which the norms of the associated automorphic forms have a different asymptotic behavior. Comment: Final version, to appear in Annals of Global Analysis and Geometry |
| Databáze: | arXiv |
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