Abstract
From the summation formulas for general Kloosterman sums and from Weil's estimates, one derives nontrivial estimates for the eigenvalues of Hecke operators, acting in the Hilbert space of parabolic forms of weight 0 relative to the group Γo(N).
Similar content being viewed by others
Literature cited
H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. II, McGraw-Hill, New York (1953).
R. C. Gunning, Lectures on Modular Forms, Princeton Univ. Press (1962).
N. V. Kuznetsov, “Petersson's conjecture,” Preprint No. 02, Habarovsk. Complex. Sci. Res. Inst., Far Eastern Scientific Center, Habarovsk (1977).
A. V. Malyshev, “On representations of integers by positive quadratic forms,” Tr. Mat. Inst. Akad. Nauk SSSR,65, Moscow-Leningrad (1962).
N. V. Proskurin, “Summation formulas for general Kloosterman sums,” J. Sov. Math.,18, No. 6 (1982).
R. W. Bruggeman, “Fourier coefficients of cusp forms,” Invent. Math.,45, No. 1, 1–18 (1978).
A. Weil, “On some exponential sums,” Proc. Nat. Acad. Sci. USA,34, 204–207 (1948).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 82, pp. 136–143, 1979.
Rights and permissions
About this article
Cite this article
Proskurin, N.V. Estimates of the eigenvalues of Hecke operators in the space of cusp forms of weight O. J Math Sci 18, 951–957 (1982). https://doi.org/10.1007/BF01763966
Issue Date:
DOI: https://doi.org/10.1007/BF01763966