A characterization of the kernel of the Poincaré series operator
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- by Makoto Masumoto PDF
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Abstract:
Let $\Gamma$ be a finitely generated Fuchsian group of the first kind acting on the unit disk $\Delta$. The kernel of the Poincaré series operator of the Hardy space ${H^p}, 1 < p < \infty$, onto the Bers space ${A_q}(\Gamma )$ of integrable holomorphic automorphic forms of weight $- 2q, q \in {\mathbf {Z}}, q \geq 2$, on $\Delta$ for $\Gamma$ is characterized in terms of Eichler integrals of order $1 - q$ on $\Delta$ for $\Gamma$.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 300 (1987), 695-704
- MSC: Primary 30F30; Secondary 11F25, 30F35
- DOI: https://doi.org/10.1090/S0002-9947-1987-0876473-5
- MathSciNet review: 876473