On integrable and bounded automorphic forms
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- by T. A. Metzger and K. V. Rajeswara Rao PDF
- Proc. Amer. Math. Soc. 28 (1971), 562-566 Request permission
Abstract:
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. Drasin and C. J. Earle, Proc. Amer. Math. Soc. 19 (1968), 1039-1042, but the present approach is entirely different. Also, using the argument of Drasin and Earle, it is proved that, for finitely generated Fuchsian groups of second kind, every integrable automorphic form of dimension $- 2$ is zero.References
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- David Drasin, Cusp forms and Poincaré series, Amer. J. Math. 90 (1968), 356–365. MR 229818, DOI 10.2307/2373532
- David Drasin and C. J. Earle, On the boundedness of automorphic forms, Proc. Amer. Math. Soc. 19 (1968), 1039–1042. MR 239083, DOI 10.1090/S0002-9939-1968-0239083-2
- Clifford J. Earle, A reproducing formula for integrable automorphic forms, Amer. J. Math. 88 (1966), 867–870. MR 206267, DOI 10.2307/2373084
- Joseph Lehner, Discontinuous groups and automorphic functions, Mathematical Surveys, No. VIII, American Mathematical Society, Providence, R.I., 1964. MR 0164033
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 562-566
- MSC: Primary 30.49
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280713-7
- MathSciNet review: 0280713