On the boundedness of $p$-integrable automorphic forms
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- by K. V. Rajeswara Rao
- Proc. Amer. Math. Soc. 44 (1974), 278-282
- DOI: https://doi.org/10.1090/S0002-9939-1974-0342693-8
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Abstract:
For a Fuchsian group, a criterion is obtained in order that every $p$-integrable automorphic form be bounded. This encompasses the known results for $p = 1$. The condition implies an interesting inequality between the Bergman kernel and the Poincaré line element of a Riemann surface.References
- Lars V. Ahlfors, Eine Bemerkung über Fuchssche Gruppen, Math. Z. 84 (1964), 244–245 (German). MR 167619, DOI 10.1007/BF01112578
- 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
- Marvin Isadore Knopp, Bounded and integrable automorphic forms, Indiana Univ. Math. J. 22 (1972/73), 769–778. MR 308391, DOI 10.1512/iumj.1973.22.22062
- Irwin Kra, Eichler cohomology and the structure of finitely generated Kleinian groups, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 225–263. MR 0286997
- Joseph Lehner, On the $A_{q}(\Gamma )\subset B_{q}(\Gamma )$ conjecture, Modular functions of one variable, I (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Lecture Notes in Math., Vol. 320, Springer, Berlin, 1973, pp. 187–194. MR 0338357 —, On the ${A_q}(\Gamma ) \subset {B_q}(\Gamma )$ conjecture in the theory of automorphic forms (to appear).
- T. A. Metzger and K. V. Rajeswara Rao, On integrable and bounded automorphic forms, Proc. Amer. Math. Soc. 28 (1971), 562–566. MR 280713, DOI 10.1090/S0002-9939-1971-0280713-7
- T. A. Metzger and K. V. Rajeswara Rao, On integrable and bounded automorphic forms. II, Proc. Amer. Math. Soc. 32 (1972), 201–204. MR 293085, DOI 10.1090/S0002-9939-1972-0293085-X
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 44 (1974), 278-282
- MSC: Primary 30A58
- DOI: https://doi.org/10.1090/S0002-9939-1974-0342693-8
- MathSciNet review: 0342693