Skip to main content
Log in

On the distribution of k-free integers

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We give two new bounds for double exponential sums of type II, by which we get new results (under RH, as before) for the distribution of k-free integers for k ≧ 5.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baker R.C.: Sums of two relatively prime cubes, Acta Arith., 129, 103–146 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baker R.C., Powell K.: The distribution of k-free numbers, Acta Math. Hungar., 126, 181–197 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  3. Graham S.W.: The distribution of square-free numbers, J. London Math. Soc., 24, 54–64 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  4. S. W. Graham and G. Kolesnik, Van der Corput’s Method of Exponential Sums, Cambridge University Press (1991).

  5. Graham S. W., Pintz J.: The distribution of r-free numbers, Acta Math. Hungar., 53, 213–236 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  6. Liu H.-Q.: On the estimates of double exponential sums. Acta Arith. 129, 203–247 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. H. L. Montgomery and R. C. Vaughan, The distribution of squarefree numbers, in: Recent Progress in Analytic Number Theory, vol. I (edited by H. Halberstam and C. Hooley) (London, 1981), pp. 247–256.

  8. O. Robert and P. Sargos, Three dimentional exponential sums with monomials, J. Reine Angew. Math., 591(2006), 1–20.

  9. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd edition, revised by D. R. Heath-Brown (Oxford, 1986).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H.-Q. Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, HQ. On the distribution of k-free integers. Acta Math. Hungar. 144, 269–284 (2014). https://doi.org/10.1007/s10474-014-0454-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-014-0454-9

Keywords and phrases

Mathematics Subject Classification

Navigation