Skip to main content
SpringerLink
Log in

The Fourth Power Mean of the General 3-dimensional Kloostermann Sums mod p

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

The main purpose of this paper is using the analytic methods, the solutions of the congruence equation mod p and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the general 3-dimensional Kloostermann sums mod p, and give a sharp asymptotic formula for it.

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

Similar content being viewed by others

References

  1. Tom, M. Apostol: Introduction to Analytic Number Theory, Springer-Verlag, New York, 1976

    Google Scholar 

  2. Mordell, L. J.: On a special polynomial congruence and exponential sums, “Calcutta Math. Soc. Golden Jubilee Commemoration Volume”, Calcutta Math. Soc, Calcutta, 29–32 (1963)

    Google Scholar 

  3. Deligne, P.: Applications de la formule des traces aux sommes trigonomtriques Cohomologie Etale, Sminaire de Gomtrie Algbrique du Bois-Marie SGA 4 1/2, Lecture Notes in Math., 569, Springer-Verlag, New York/Berlin, 168–232, 1977

    Google Scholar 

  4. Zhang, W. P., Han, D.: A new identity involving the classical Kloosterman sums and 2-dimensional Kloostermann sums. Internatonal Journal of Number Theory, 12, 111–119 (2016)

    Article  MATH  Google Scholar 

  5. Wolfgang, M. Schmidt: Equations over Finite Fields An Elementary Approach, Springer-Verlag, New York, pp. 92, 1976

    Google Scholar 

  6. Smith, R. A.: On n-dimensional Kloostermann sums. Journal of Number Theory, 11, 324–343 (1979)

    Article  MathSciNet  Google Scholar 

  7. Luo, W.: Bounds for incomplete Kloostermann sums. Journal of Number Theory, 75, 41–46 (1999)

    Article  MathSciNet  Google Scholar 

  8. Shparlinski, I. E.: Bounds of incomplete multiple Kloostermann sums. Journal of Number Theory, 126, 68–73 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ye, Y.: Identities of incomplete Kloostermann sums. Proc. Amer. Math. Soc., 127, 2591–2600 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Malyshev, A. V.: A generalization of Kloosterman sums and their estimates (in Russian). Vestnik Leningrad University, 15, 59–75 (1960)

    MathSciNet  Google Scholar 

  11. Zhang, W., Li, X.: The fourth power mean of the general 2-dimensional Kloostermann sums mod p. Acta Mathematica Sinica English Series, 33, 861–867 (2017)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to sincerely thank the anonymous referee for his careful reading of the manuscript and valuable comments.

Author information

Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710049, P. R. China

    Wen Peng Zhang & Xing Xing Lv

Authors
  1. Wen Peng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xing Xing Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen Peng Zhang.

Additional information

Supported by NSF (Grant No. 11771351)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, W.P., Lv, X.X. The Fourth Power Mean of the General 3-dimensional Kloostermann Sums mod p. Acta. Math. Sin.-English Ser. 35, 369–377 (2019). https://doi.org/10.1007/s10114-018-7455-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-018-7455-5

Keywords

MR(2010) Subject Classification

Search

Navigation