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Norms of integrable cusp forms


Author: L. Alayne Parson
Journal: Proc. Amer. Math. Soc. 104 (1988), 1045-1049
MSC: Primary 11F11
DOI: https://doi.org/10.1090/S0002-9939-1988-0935108-X
MathSciNet review: 935108
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Abstract: The norms of modular cusp forms, viewed as belonging to the Bers' spaces of integrable and bounded forms, are estimated in terms of the Fourier coefficients of the cusp form.


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

  • [1] H. Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent. Math. 87 (1987), 385-401. MR 870736 (88b:11024)
  • [2] L. A. Parson, A lower bound for the norm of the theta operator, Math. Comp. 41 (1983), 683-685. MR 717712 (85d:30073)
  • [3] -, Generalized Kloosterman sums and the Fourier coefficients of cusp forms, Trans. Amer. Math. Soc. 217 (1976), 329-350. MR 0412112 (54:241)
  • [4] R. A. Rankin, Modular forms and functions, Cambridge Univ. Press, Cambridge, 1977. MR 0498390 (58:16518)
  • [5] R. A. Smith, The $ {L^2}$-norm of Maass wave functions, Proc. Amer. Math. Soc. 82 (1981), 179-182. MR 609646 (82f:10029)
  • [6] D. B. Zagier, Modular forms whose Fourier coefficients involve zeta-functions of guadratic fields, Modular Functions of One Variable VI (J.-P. Serre and D. B. Zagier eds.), Springer Lecture Notes, no. 627, 1977, 105-169. MR 0485703 (58:5525)

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DOI: https://doi.org/10.1090/S0002-9939-1988-0935108-X
Article copyright: © Copyright 1988 American Mathematical Society

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