Skip to main content
SpringerLink
Log in

On the Fourth Power Mean of the Character Sums Over Short Intervals

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

Abstract

The main purpose of this paper is to study the mean value properties of the character sums over the interval \( \left[ {1,\;{p \over 8}} \right) \)by using the mean value theorems of the Dirichlet L-functions, and give an interesting mean value formula for this study.

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. Pólya, G.: Über die Verteilung der quadratische Reste und Nichtreste, Göttingen Nachrichten, 21–29, 1918

  2. Vinogradov, I. M.: On the diswtribution of residues and non-residues of powers. Journal of the Physico-Mathematical Society of Perm, 1, 94–96 (1918)

    Google Scholar 

  3. Sokolovskii, A. V.: On a theorem of Sárkozy. Acta Arithmetica, 41, 27–31 (1982)

    MathSciNet  Google Scholar 

  4. Burgess, D. A.: On a conjecture of Norton. Acta Arithmetica, 27, 265–267 (1975)

    MathSciNet  MATH  Google Scholar 

  5. Norton, K. K.: On character sums and power residues. Trans. Amer. Math. Soc., 167, 203–226 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  6. Burgess, D. A.: Mean value of character sums. Mathematika, 33, 1–5 (1986)

    MathSciNet  MATH  Google Scholar 

  7. Burgess, D. A.: Mean value of character sums II. Mathematika, 33, 1–7 (1987)

    Article  Google Scholar 

  8. C. Peral, J.: Character sums and explicit estimates for L-functions. Contemporary Mathematics, 189, 449–459 (1995)

    MathSciNet  Google Scholar 

  9. Zhang, W. P.: On a Cochrane sum and its hybrid mean value formula (II). Journal of Mathematical Analysis and Applications, 276, 446–457, (2002)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zhang, W. P., Yi, Y., He X L.: On the 2k-th power mean of Dirichlet L-functions with the weight of general Kloosterman sums. Journal of Number Theory, 84, 199–213 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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

  12. Pan, C. D., Pan, C. B.: Goldbach Conjecture, Science Press, Beijing, 1981

Download references

Author information

Authors and Affiliations

  1. Research Center for Basic Science, Xi'an Jiaotong University, Xi’an 710049, P. R. China

    Wen Peng Zhang & Xiao Ying Wang

Authors
  1. Wen Peng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao Ying Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen Peng Zhang.

Additional information

This work is supported by the N.S.F. (10271093) of P. R. China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, W.P., Wang, X.Y. On the Fourth Power Mean of the Character Sums Over Short Intervals. Acta Math Sinica 23, 153–164 (2007). https://doi.org/10.1007/s10114-005-0893-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-005-0893-x

Keywords

MR (2000) Subject Classification

Search

Navigation