@article{SM_2001_192_8_a6,
author = {V. N. Sorokin},
title = {On linear independence of values of generalized polylogarithms},
journal = {Sbornik. Mathematics},
pages = {1225--1239},
year = {2001},
volume = {192},
number = {8},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2001_192_8_a6/}
}
V. N. Sorokin. On linear independence of values of generalized polylogarithms. Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1225-1239. http://geodesic.mathdoc.fr/item/SM_2001_192_8_a6/
[1] Shidlovskii A. B., Diofantovy priblizheniya i transtsendentnye chisla, Izd-vo MGU, M., 1982 | MR
[2] Gonchar A. A., Rakhmanov E. A., Sorokin V. N., “Approksimatsii Ermita–Pade dlya sistem funktsii markovskogo tipa”, Matem. sb., 188:5 (1997), 33–58 | MR | Zbl
[3] Minh H. N., Petitot M., “Lyndon words, polylogarithms and Riemann $\zeta$ function”, Discrete Math., 217:1–3 (2000), 273–292 ; Formal Power Series and Algebraic Combinatorics (Vienna, 1997) | DOI | MR | Zbl
[4] Minh H. N., Petitot M., Van Der Hoeven J., Shuffle algebra and polylogarithms, Preprint, 1998; Formal Power Series and Algebraic Combinatorics (Toronto, June 1998)
[5] Nikishin E. M., “Ob irratsionalnosti znachenii funktsii $F(x,s)$”, Matem. sb., 109 (151):3 (1979), 410–418 | MR
[6] Sorokin V. N., “Approksimatsii Ermita–Pade posledovatelnykh stepenei logarifma i ikh arifmeticheskie prilozheniya”, Izv. vuzov. Ser. matem., 1991, no. 11, 66–74 | MR
[7] Mahler K., “Zur Approximation der Exponentialfunktion und des Logarithmus”, J. Reine Angew. Math., 166 (1932), 118–150
[8] Sorokin V. N., “O mere transtsendentnosti chisla $\pi^2$”, Matem. sb., 187:12 (1996), 87–120 | MR | Zbl
[9] Sorokin V. N., “O teoreme Aperi”, Vestn. MGU. Ser. 1. Matem., mekh., 1998, no. 3, 48–53 | MR | Zbl
[10] Hata M., “Rational approximations to the dilogarithm”, Trans. Amer. Math. Soc., 336:1 (1993), 363–387 | DOI | MR | Zbl
[11] Mahler K., “Perfect systems”, Compositio Math., 19 (1968), 95–166 | MR | Zbl