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Journal Article

# A Characterization of the Kernel of the Poincaré Series Operator

Makoto Masumoto
Transactions of the American Mathematical Society
Vol. 300, No. 2 (Apr., 1987), pp. 695-704
DOI: 10.2307/2000364
Stable URL: http://www.jstor.org/stable/2000364
Page Count: 10
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## Abstract

Let Γ be a finitely generated Fuchsian group of the first kind acting on the unit disk Δ. The kernel of the Poincaré series operator of the Hardy space $H^p, 1 < p < \infty$, onto the Bers space Aq(Γ) of integrable holomorphic automorphic forms of weight -2q, q ∈ Z, q ≥ 2, on Δ for Γ is characterized in terms of Eichler integrals of order 1 - q on Δ for Γ.

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