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, access via your institution.
Buy single article
Instant access to the full article PDF.
Price includes VAT (USA)
Tax calculation will be finalised during checkout.
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).
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).
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).
E. M. Nikishin, “On logarithms of natural numbers,” Izv. Akad. Nauk SSSR, Ser. Mat., 43, No. 6, 1319–1327 (1979); 44, 972 (1980).
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).
V. N. Sorokin, “On linear independence of values of generalized polylogarithms,” Mat. Sb., 192, No. 8, 139–154 (2001).
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 179–194, 2005.
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
- Linear Form
- Rational Number
- Algebraic Number
- Laurent Series
- Monodromy Group