FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 6, PAGES 179-194

**Estimates for polynomials in logarithms of some rational numbers**

V. N. Sorokin

Abstract

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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.

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Last modified: January 13, 2006