Inventiones mathematicae

, Volume 115, Issue 1, pp 209–217 | Cite as

A quadratic divisor problem

  • W. Duke
  • J. B. Friedlander
  • H. Iwaniec
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [DeI1] Deshouillers J.-M., Iwaniec, H: An additive divisor problem. J. London Math. Soc.26, 1–14 (1982)Google Scholar
  2. [DeI2] Deshouillers J.-M. Iwaniec, H.: Kloosterman sums and Fourier coefficients of cusp forms. Invent. Math70, 219–288 (1982)Google Scholar
  3. [DFI1] Duke, W., Friedlander, J., Iwaniec, H.: Bounds for automorphicL-functions. Invent. Math.112, 1–8 (1993)Google Scholar
  4. [DFI2] Duke, W., Friedlander, J., Iwaniec H: Bounds for automorphicL-functions II Invent. Math.115, 219–239 (1994)Google Scholar
  5. [DuI] Duke, W., Iwaniec, H.: ConvolutionL-series (to appear)Google Scholar
  6. [Es] Estermann, T.: Über die Darstellung einer Zahl als Differenz von swei Produkten. J. Reine Angew. Math.164, 173–182 (1931)Google Scholar
  7. [Ha] Hafner, J.L.: Explicit estimates in the arithmetic theory of Poincaré series, Math. Ann.264, 9–20 (1983)Google Scholar
  8. [HB] Heath-Brown, D.R.: The fourth power moment of the Riemann zeta-function, Proc. London Math. Soc.38, 385–422 (1979)Google Scholar
  9. [He] Hejhal, D.: Sur certaines séries de Dirichlet dont les pôles sont sur les lignes critiques. CR Acad. Sci. Paris, Sér A287, 383–385 (1978)Google Scholar
  10. [In] Ingham, A.E.: Some asymptotic formulae in the theory of numbers. J. London Math. Soc.2, 202–208 (1927)Google Scholar
  11. [Ju1] Jutila, M: A method in the theory of exponential sums, Tata Lect. Notes Math.80, Bombay (1987)Google Scholar
  12. [Ju2] Jutila, M.: The additive divisor problem and exponential sums. In: Advances in Number Theory, 113–135. Proc Conf. Kingston Ont., 1991, Oxford (1993)Google Scholar
  13. [Kl] Kloosterman, H.D.: On the representation of numbers in the formax 2+by 2+cz 2+dt 2. Acta Math.49, 407–464 (1926)Google Scholar
  14. [Ku] Kuznetsov, N.V.: Convolution of the Fourier coefficients of the Eisenstein-Maass series. Zap. Nauk Sem. LOMI129, 43–84 (1983)Google Scholar
  15. [Mo] Motohashi, Y: The binary additive divisor problem (to appear).Google Scholar
  16. [Ra] Rademacher, H.: Topics in Analytic Number Theory, New York: Springer 1973Google Scholar
  17. [Sm] Smith, R.A.: The circle problem in an arithmetic progression, Can. Math. Bull.11, 175–184 (1968)Google Scholar
  18. [Wa] Watt, N: (preprint).Google Scholar
  19. [Wi] Wirsing, E: (unpublished manuscript).Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • W. Duke
    • 1
    • 2
  • J. B. Friedlander
    • 1
    • 2
  • H. Iwaniec
    • 1
    • 2
  1. 1.Department of MathematicsRutgers UniversityNew BrunswichUSA
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

Personalised recommendations