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On integrable and bounded automorphic forms
Proceedings of the American Mathematical Society
A necessary and sufficient condition that every integrable automorphic form of dimension < -2 be a bounded form is established. Using this condition, it is shown that, for a finitely generated Fuchsian group acting on the unit disc and containing no parabolic elements, every integrable automorphic form of dimension < -2 is bounded. Here the dimension is not required to be integral. In the case of even integral dimension and standard factors of automorphy, this latter result is contained in D.doi:10.1090/s0002-9939-1971-0280713-7 fatcat:yc3fd2lh3zck7jfsyjv763zkre