On linear independence of values of generalized polylogarithms
Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1225-1239 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
@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/}
}
TY  - JOUR
AU  - V. N. Sorokin
TI  - On linear independence of values of generalized polylogarithms
JO  - Sbornik. Mathematics
PY  - 2001
SP  - 1225
EP  - 1239
VL  - 192
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_2001_192_8_a6/
LA  - en
ID  - SM_2001_192_8_a6
ER  - 
%0 Journal Article
%A V. N. Sorokin
%T On linear independence of values of generalized polylogarithms
%J Sbornik. Mathematics
%D 2001
%P 1225-1239
%V 192
%N 8
%U http://geodesic.mathdoc.fr/item/SM_2001_192_8_a6/
%G en
%F 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