Inventiones mathematicae

, Volume 71, Issue 2, pp 243–250

Sums of Kloosterman sums

  • D. Goldfeld
  • P. Sarnak
Article

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References

  1. 1.
    Bruggeman, R.W.: Fourier coefficients of cusp forms. Invent. Math.45, 1–18 (1978)Google Scholar
  2. 2.
    Davenport, H.: On certain exponential sums. J. für Mathematik169, 158 (1933)Google Scholar
  3. 3.
    Davenport, H.: Multiplicative number theory. Berlin-Heidelberg-New York: Springer 1980Google Scholar
  4. 4.
    Deshouillers, J.M., Iwaniec, H.: Kloosterman sums and Fourier coefficients of cusp forms. Preprint 1981Google Scholar
  5. 5.
    Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series, and products. New York: Academic Press 1980Google Scholar
  6. 6.
    Hardy, G., Riesz, M.: Dirichlet series. Cambridge: Cambridge University Press 1915Google Scholar
  7. 7.
    Kuznetsov, N.V.: Peterson hypothesis, for parabolic forms of weight zero and Linnik hypothesis. Sums of Kloosterman sums. Math. Sbornik111, (153, no. 3) 334–383 (1980)Google Scholar
  8. 8.
    Linnik, Y.V.: Additive problems and eigenvalues of the modular operators. Proc. Internat. Congr. Math. Stockholm 1962, pp. 270–284Google Scholar
  9. 9.
    Proskurin, N.V.: Summation formulas for generalized Kloosterman sums. Zap. Navcn. Sem. Leningrad Otdel. Mat. Inst. Steklov82, 103–135 (1979)Google Scholar
  10. 10.
    Riesz, F., Nagy, B.: Functional analysis. New York: Frederick Ungar Publishing Company 1978Google Scholar
  11. 11.
    Roelcke, W.: Das Eigenwertproblem der automorphen Formen... Math. Ann.167, 292–337 (1966)Google Scholar
  12. 12.
    Selberg, A.: On the estimation of Fourier coefficients of modular forms. Proc. Symposia in Pure Math. VIII. A.M.S., Providence 1965, pp. 1–15.Google Scholar
  13. 13.
    Vardi, I.: Mass. Inst. Tech. Ph.D. Thesis, 1982Google Scholar
  14. 14.
    Weil, A.: On some exponential sums. Proc. Natl. Acad. Sci. USA34, 204–207 (1948)Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • D. Goldfeld
    • 1
  • P. Sarnak
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Courant Institute of Mathematical SciencesNew YorkUSA

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