Skip to main content
SpringerLink
Log in

Large families of subsets arising from Woods problem and their pseudorandomness

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We introduce large families of subsets arising from Woods problem and study their cardinalities. Estimates of character sums over the subsets are given. We study the pesudorandom properties of the subsets and show that their well-distribution measures are very high.

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. Chen Z.: Large families of pseudo-random subsets formed by generalized cyclotomic classes. Monatsh. Math., 161, 161–172 (2010)

    Article  MathSciNet  Google Scholar 

  2. Dartyge C., Mosaki E., Sárközy A.: On large families of subsets of the set of the integers not exceeding N. Ramanujan J., 18, 209–229 (2009)

    Article  MathSciNet  Google Scholar 

  3. Dartyge C., Sárközy A.: On pseudo-random subsets of the set of the integers not exceeding N. Periodica Math. Hungar., 54, 183–200 (2007)

    Article  MathSciNet  Google Scholar 

  4. Dartyge C., Sárközy A.: Large families of pseudorandom subsets formed by power residues. Unif. Distrib. Theory, 2, 73–88 (2007)

    MathSciNet  MATH  Google Scholar 

  5. Dartyge C., Sárközy A., Szalay M.: On the pseudo-randomness of subsets related to primitive roots. Combinatorica, 30, 139–162 (2010)

    Article  MathSciNet  Google Scholar 

  6. Liu H.: Large family of pseudorandom subsets of the set of the integers not exceeding N. Int. J. Number Theory, 10, 1121–1141 (2014)

    Article  MathSciNet  Google Scholar 

  7. Liu H., Song E.: A note on pseudorandom subsets formed by generalized cyclotomic classes. Publ. Math. Debrecen, 85, 257–271 (2014)

    Article  MathSciNet  Google Scholar 

  8. Weil A.: On some exponential sums. Proc. Nat. Acad. Sci., 34, 204–207 (1948)

    Article  MathSciNet  Google Scholar 

  9. Xi P., Yi Y.: On character sums over flat numbers. J. Number Theory, 130, 1234–1240 (2010)

    Article  MathSciNet  Google Scholar 

  10. Xu Z.: Distribution of the difference of an integer and its m-th power mod n over incomplete intervals. J. Number Theory, 133, 4200–4223 (2013)

    Article  MathSciNet  Google Scholar 

  11. Zhang W.: On a problem of A. C. Woods. Adv. Math. (China), 23, 284–285 (1994)

    MATH  Google Scholar 

  12. Zhang W.: Some estimates of trigonometric sums and their application. Acta Math. Hungar., 76, 17–30 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, Shaanxi, P. R. China

    Y. Cao & H. Liu

Authors
  1. Y. Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Liu.

Additional information

This work is supported by National Natural Science Foundation of China under Grant No. 11571277, and the Science and Technology Program of Shaanxi Province of China under Grant No. 2016GY-080 and 2016GY-077.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, Y., Liu, H. Large families of subsets arising from Woods problem and their pseudorandomness. Acta Math. Hungar. 156, 204–219 (2018). https://doi.org/10.1007/s10474-018-0834-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-018-0834-7

Keywords and phrases

Mathematics Subject Classification

Search

Navigation