Skip to main content
SpringerLink
Log in

Sums of Kloosterman sums

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bruggeman, R.W.: Fourier coefficients of cusp forms. Invent. Math.45, 1–18 (1978)

    Google Scholar 

  2. Davenport, H.: On certain exponential sums. J. für Mathematik169, 158 (1933)

    Google Scholar 

  3. Davenport, H.: Multiplicative number theory. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  4. Deshouillers, J.M., Iwaniec, H.: Kloosterman sums and Fourier coefficients of cusp forms. Preprint 1981

  5. Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series, and products. New York: Academic Press 1980

    Google Scholar 

  6. Hardy, G., Riesz, M.: Dirichlet series. Cambridge: Cambridge University Press 1915

    Google Scholar 

  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. Linnik, Y.V.: Additive problems and eigenvalues of the modular operators. Proc. Internat. Congr. Math. Stockholm 1962, pp. 270–284

  9. Proskurin, N.V.: Summation formulas for generalized Kloosterman sums. Zap. Navcn. Sem. Leningrad Otdel. Mat. Inst. Steklov82, 103–135 (1979)

    Google Scholar 

  10. Riesz, F., Nagy, B.: Functional analysis. New York: Frederick Ungar Publishing Company 1978

    Google Scholar 

  11. Roelcke, W.: Das Eigenwertproblem der automorphen Formen... Math. Ann.167, 292–337 (1966)

    Google Scholar 

  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.

  13. Vardi, I.: Mass. Inst. Tech. Ph.D. Thesis, 1982

  14. Weil, A.: On some exponential sums. Proc. Natl. Acad. Sci. USA34, 204–207 (1948)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    D. Goldfeld

  2. Courant Institute of Mathematical Sciences, 10012, New York, NY, USA

    P. Sarnak

Authors
  1. D. Goldfeld
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Sarnak
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goldfeld, D., Sarnak, P. Sums of Kloosterman sums. Invent Math 71, 243–250 (1983). https://doi.org/10.1007/BF01389098

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01389098

Search

Navigation