Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A characterization of the kernel of the Poincaré series operator


Author: Makoto Masumoto
Journal: Trans. Amer. Math. Soc. 300 (1987), 695-704
MSC: Primary 30F30; Secondary 11F25, 30F35
MathSciNet review: 876473
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30F30, 11F25, 30F35

Retrieve articles in all journals with MSC: 30F30, 11F25, 30F35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0876473-5
PII: S 0002-9947(1987)0876473-5
Keywords: Poincaré series, automorphic form, Eichler integral
Article copyright: © Copyright 1987 American Mathematical Society