Geodesic
Estimates for polynomials in logarithms of some rational numbers
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 179-194 
V. N. Sorokin. Estimates for polynomials in logarithms of some rational numbers. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 179-194. http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a14/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Galochkin A. I., “Otsenki snizu mnogochlenov ot znachenii analiticheskikh funktsii odnogo klassa”, Mat. sb., 95(137):3(11) (1974), 396–417 | Zbl

[2] Gonchar A. A., Rakhmanov E. A., Sorokin V. N., “Ob approksimatsiyakh Ermita–Pade dlya sistem funktsii markovskogo tipa”, Mat. sb., 188:5 (1997), 33–58 | MR | Zbl

[3] Nikishin E. M., “O logarifmakh naturalnykh chisel”, Izv. AN SSSR. Ser. mat., 43:6 (1979), 1319–1327 ; 44 (1980), 972 | MR | Zbl | MR | Zbl

[4] Sorokin V. N., “O lineinoi nezavisimosti znachenii obobschënnykh polilogarifmov”, Mat. sb., 192:8 (2001), 139–154 | MR | Zbl

[5] Feldman N. I., “Ob otsenke modulya lineinoi formy ot logarifmov nekotorykh algebraicheskikh chisel”, Mat. zametki, 2:3 (1967), 245–256 | MR

[6] Shidlovskii A. B., “O kriterii algebraicheskoi nezavisimosti znachenii odnogo klassa tselykh funktsii”, Izv. AN SSSR. Ser. mat., 23 (1959), 35–66 | Zbl