On linear independence of values of generalized polylogarithms
Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1225-1239
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The linear independence of the values at certain rational points of generalized polylogarithms, which generate the algebra of all analytic functions with three logarithmic branch points, is established. Hermite–Padé approximations for an Angelesco–Nikishin system defined by a complete binary tree are used.

[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