Skip to main content
SpringerLink
Log in

On the distribution of αp modulo one (II)

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

Suppose that α is an irrational number and β is a real number. It is proved that there are infinitely many prime numbers p such that ‖ αp-β‖ <p -9/28.

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. Vinogradov, I. M., The Method of Trigonometric Sums in the Theoiy of Numbers, London: Wiley-Interscience, 1954.

    Google Scholar 

  2. Vaughan, R., On the distribution of αp modulo 1, Mathematika, 1977, 24: 135.

    Article  MathSciNet  Google Scholar 

  3. Harman, G., On the distribution of αp modulo one, J. London Math. Soc., 1983, 27(2): 9.

    Article  MATH  MathSciNet  Google Scholar 

  4. Jia, C, On the distribution of αp modulo one, J. Number Theory, 1993, 45: 241.

    Article  MATH  MathSciNet  Google Scholar 

  5. Harman, G., On the distribution of αp modulo one II, Proc. London Math. Soc., 1996, 72(3): 241.

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen, J., On the Goldbach's problem and the sieve methods, Sci. Sin., 1978, 21: 701.

    MATH  Google Scholar 

  7. Jia, C., Almost all short intervals containing prime numbers, Acta Arith., 1996, 76: 21.

    MathSciNet  Google Scholar 

  8. Pan, D., Pan, B., Goldbach Conjecture (in Chinese), Beijing: Science Press, 1981.

    Google Scholar 

  9. Jia, C., On Pjateckiľ-Šapiro prime number theorem (II), Science in China, Ser. A, 1993, 36: 913.

    MATH  Google Scholar 

  10. Balog, A., On the distribution of pθ mod 1, Acta Math. Hung., 1985, 45(1-2): 179.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chinese Academy of Sciences, Institute of Mathematics, 100080, Beijing, China

    Chaohua Jia

Authors
  1. Chaohua Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chaohua Jia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jia, C. On the distribution of αp modulo one (II). Sci. China Ser. A-Math. 43, 703–721 (2000). https://doi.org/10.1007/BF02878436

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02878436

Keywords

Search

Navigation