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Annals of Global Analysis and Geometry

, Volume 55, Issue 3, pp 417–441 | Cite as

On vector-valued automorphic forms on bounded symmetric domains

  • Nadia Alluhaibi
  • Tatyana BarronEmail author
Article

Abstract

We prove a spanning result for vector-valued Poincaré 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 \({\mathbb {C}}^n\), 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 behaviour.

Keywords

Holomorphic automorphic forms Poincaré series Spanning set Domain Canonical bundle Bergman kernel Complex hyperbolic space Submanifold Asymptotics 

Mathematics Subject Classification

32N15 53C99 

Notes

Acknowledgements

We are thankful to A. Dhillon, Y. Karshon, M. Pinsonnault, E. Schippers, A. Uribe, and N. Yui for related discussions. We acknowledge the referee’s efforts.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Science and Arts College, Rabigh CampusKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of MathematicsUniversity of Western OntarioLondonCanada

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