Proceedings of the American Mathematical Society

Author(s): Tatyana Foth
Journal: Proc. Amer. Math. Soc. 135 (2007), 3301-3308.
MSC (2000): Primary 32N10; Secondary 32N05, 32N15
Posted: June 21, 2007
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Abstract: We show that any holomorphic automorphic form of sufficiently large weight on an irreducible bounded symmetric domain in ${\mathbb{C}}^n$ ,

, is the Poincaré series of a polynomial in

,...,

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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