Skip to main content
SpringerLink
Log in

A note on the hyper Cochrane sum

  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

The main purpose of this paper is using the analytic methods to study the upper bound of the hyper Cochrane sum, and obtain an interesting result which generalized the main theorem of Liu [2].

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. T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York (1976).

    Book  MATH  Google Scholar 

  2. H. N. Liu, A note on the upper bound estimate of high-dimensional Cochrane sums, J. Number Theory, 125 (2007), 7–13.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Xie and W. P. Zhang, On the 2k-th mean value formula of general Dedekind sums, Acta Math. Sinica (Chin. Ser.), 26 (2001), 85–94.

    MathSciNet  Google Scholar 

  4. Z. F. Xu and W. P. Zhang, On the order of the high-dimensional Cochrane sums and its mean value, J. Number Theory, 117 (2006), 131–145.

    Article  MathSciNet  MATH  Google Scholar 

  5. L. Weinstein, The hyper-Kloosterman sum, Enseign. Math., 27 (1981), 29–40.

    MathSciNet  MATH  Google Scholar 

  6. T. P. Zhang and W. P. Zhang, Hyper Cochrane sums and their hybrid mean value formula, Chinese Ann. Math. Ser. A, 26 (2005), 469–476.

    MathSciNet  MATH  Google Scholar 

  7. T. P. Zhang and W. P. Zhang, On the r-th hyper-Kloosterman sums and its hybrid mean value, J. Korean Math. Soc., 43 (2006), 1199–1217.

    Article  MathSciNet  MATH  Google Scholar 

  8. W. P. Zhang, On the general Dedekind sums and one kind identities of Dirichlet L-functions, Acta Math. Sin. (Engl. Ser.), 44 (2001), 269–272.

    MATH  Google Scholar 

  9. W. P. Zhang and Y. Yi, On the upper bound estimate of Cochrane sums, Soochow J. Math., 28 (2002), 297–304.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, Shaanxi, P. R. China

    Tianping Zhang

Authors
  1. Tianping Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tianping Zhang.

Additional information

This work is supported by National Natural Science Foundation of China (No. 11201275), the Mathematical Tianyuan Foundation (No. 11126199), Natural Science Foundation of Shaanxi province of China (No. 2011JQ1010), the Natural Science Foundation of the Education Department of Shaanxi Province of China (No. 09JK803) and the Fundamental Research Funds for the Central Universities (No. GK200902051).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, T. A note on the hyper Cochrane sum. Indian J Pure Appl Math 44, 297–310 (2013). https://doi.org/10.1007/s13226-013-0015-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-013-0015-x

Key words

Search

Navigation