Skip to main content
SpringerLink
Log in

Estimates for polynomials in logarithms of some rational numbers

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The Hermite-Pade approximations of the second type for algebra generated by a generalized Nikishin system of Markov functions corresponding to an infinite branching graph are investigated. Arithmetical applications of this construction are given. Namely, lower estimates for polynomials with integer coefficients in logarithms of some rational numbers are obtained. These estimates partially refine some known results obtained earlier by the Siegel method.

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. N. I. Fel’dman, “On the estimation of the module of the linear form of logarithms of some algebraic numbers,” Mat. Zametki, 2, No. 3, 245–256 (1967).

    MathSciNet  Google Scholar 

  2. A. I. Galochkin, “Low estimations of polynomials of values of analytic functions from some class,” Mat. Sb., 95(137), No. 3 (11), 396–417 (1974).

    MathSciNet  Google Scholar 

  3. A. A. Gonchar, E. A. Rakhmanov, and V. N. Sorokin, “On Hermite-Pade approximants for systems of Markov type functions,” Mat. Sb., 188, No. 5, 33–58 (1997).

    MathSciNet  Google Scholar 

  4. E. M. Nikishin, “On logarithms of natural numbers,” Izv. Akad. Nauk SSSR, Ser. Mat., 43, No. 6, 1319–1327 (1979); 44, 972 (1980).

    MATH  MathSciNet  Google Scholar 

  5. A. B. Shidlovskii, “On criteria of algebraic independence of values of one class of entire functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 23, 35–66 (1959).

    MathSciNet  Google Scholar 

  6. V. N. Sorokin, “On linear independence of values of generalized polylogarithms,” Mat. Sb., 192, No. 8, 139–154 (2001).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State University, Russia

    V. N. Sorokin

Authors
  1. V. N. Sorokin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. N. Sorokin.

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 179–194, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sorokin, V.N. Estimates for polynomials in logarithms of some rational numbers. J Math Sci 146, 5759–5770 (2007). https://doi.org/10.1007/s10958-007-0390-0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-007-0390-0

Keywords

Search

Navigation