Skip to main content
SpringerLink
Log in

A numerical bound for small prime solutions of some binary equations

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

Abstract

In this paper we consider the linear equation a1p1 +a2p2 = n in prime variables pi and estimate the numerical value of a relevant constant in the upper bound for small prime solutions of the above equation in terms of max ai.

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. Montgomery, H. L., Vaughan, R. C., The exceptional set in Goldbach’s problem, Acta Arith., 1975, 27: 353–370.

    MATH  MathSciNet  Google Scholar 

  2. Chen, J. R., Pan, C. D., The exceptional set of Goldbach numbers, Sci. Sinica, 1980, 23: 416–430.

    MathSciNet  Google Scholar 

  3. Li, H. Z., The exceptional set of Goldbach numbers (II), Acta Arith., 2000, 92: 71–88.

    MATH  MathSciNet  Google Scholar 

  4. Liu, M. C., An improved bound for prime solutions of some ternary equations, Math. Z., 1987, 194: 573–583.

    Article  MATH  MathSciNet  Google Scholar 

  5. Liu, M. C., Tsang, K. M., Small prime solutions of linear equations, Théorie des Nombres, Walter de Gruyter, 1989, 595–624.

  6. Liu, M. C., Wang, T. Z., A numerical bound for small prime solutions of some ternary linear equations, Acta Arith., 1998, 86: 343–383.

    MATH  MathSciNet  Google Scholar 

  7. Pan, C. D., Pan, C. B., Goldbach Conjecture, Beijing: Science Press, 1992.

    MATH  Google Scholar 

  8. Li, H. Z., The exceptional set of Goldbach numbers, Quart. J. Math., 1999, 50: 471–482

    Article  MATH  Google Scholar 

  9. Heath-Brown, D. R., The density of zeros of Dirichlet’s L-functions, Can. J. Math., 1979, 31: 231–240.

    MATH  MathSciNet  Google Scholar 

  10. Li, H. Z., Zero-free regions for Dirichlet L-functions, Quart. J. Math. Oxford, 1999, 50: 13–23.

    Article  MATH  Google Scholar 

  11. Gallagher, P. X., A large sieve estimate near σ = 1, Invent. Math., 1970, 11: 329–339.

    Article  MATH  MathSciNet  Google Scholar 

  12. Chen, J. R., Liu, J. M., The exceptional set of Goldbach numbers (III), Quart. J. Math. (in Chinese), 1989,4: 1–15.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiaotong University, 200030, Shanghai, China

    Hongze Li

Authors
  1. Hongze Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongze Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, H. A numerical bound for small prime solutions of some binary equations. Sci. China Ser. A-Math. 46, 48–63 (2003). https://doi.org/10.1360/03ys9006

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1360/03ys9006

Keywords

Search

Navigation