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Poincaré series on bounded symmetric domains

Author: Tatyana Foth
Journal: Proc. Amer. Math. Soc. 135 (2007), 3301-3308
MSC (2000): Primary 32N10; Secondary 32N05, 32N15
Published electronically: June 21, 2007
MathSciNet review: 2322762
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Abstract: We show that any holomorphic automorphic form of sufficiently large weight on an irreducible bounded symmetric domain in $ {\mathbb{C}}^n$, $ n>1$, is the Poincaré series of a polynomial in $ z_1$,...,$ z_n$ and give an upper bound for the degree of this polynomial. We also give an explicit construction of a basis in the space of holomorphic automorphic forms.

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Additional Information

Tatyana Foth
Affiliation: Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada

Received by editor(s): October 6, 2005
Received by editor(s) in revised form: July 25, 2006
Published electronically: June 21, 2007
Additional Notes: The research of this author was supported in part by NSF grant DMS-0204154
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2007 American Mathematical Society