Skip to main content
Log in

Symmetrized version of the Markovecchio integral in the theory of Diophantine approximations

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

A new integral construction unifying the idea of symmetry proposed by Salikhov in 2007 and the integral introduced by Markovecchio in 2009 is considered. The application of this construction leads, in particular, to a sharper estimate of the measure of irrationality of the number π/√3.

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. V. Kh. Salikhov, “On the irrationalitymeasure of log 3,” Dokl.Ross. Akad.Nauk Russian Academy of Sciences 417 (6), 753–755 (2007) [Dokl. Math. 76 (3), 955–957 (2007)].

    MathSciNet  Google Scholar 

  2. V. Kh. Salikhov, “On the measure of irrationality of the number π,” Mat. Zametki 88 (4), 583–593 (2010) [Math. Notes 88 (3–4), 563–573 (2010)].

    Article  MathSciNet  Google Scholar 

  3. R. Marcovecchio, “The Rhin–Viola method for log 2,” Acta Arith. 139 (2), 147–184 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Rhin and C. Viola, “On a permutation group related to ζ(2),” Acta Arith. 77 (1), 23–56 (1996).

    MATH  MathSciNet  Google Scholar 

  5. G. Rhin and C. Viola, “The group structure for ζ(3),” Acta Arith. 97 (3), 269–293 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  6. Yu. V. Nesterenko, “On the irrationality exponent of the number ln 2,” Mat. Zametki 88 (4), 549–564 (2010) [Math. Notes 88 (3–4), 530–543 (2010)].

    Article  MathSciNet  Google Scholar 

  7. H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 1: The Hypergeometric Function, Legendre Functions (McGraw–Hill, New York–Toronto–London, 1953; Nauka, Moscow, 1973).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Androsenko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Androsenko, V.A., Salikhov, V.K. Symmetrized version of the Markovecchio integral in the theory of Diophantine approximations. Math Notes 97, 493–501 (2015). https://doi.org/10.1134/S0001434615030219

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434615030219

Keywords

Navigation