Geodesic
Expansion of Multiple Integrals in Linear Forms
Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 683-706.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove general theorems on expansions of multiple integrals in linear forms in generalized polylogarithms with coefficients that are rational functions. 
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S. A. Zlobin. Expansion of Multiple Integrals in Linear Forms. Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 683-706. http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a3/

[1] Beukers F., “A note on the irrationality of $\zeta(2)$ and $\zeta(3)$”, Bull. London Math. Soc., 11:3 (1979), 268–272 | DOI | MR | Zbl

[2] Vasilenko O. N., “Nekotorye formuly dlya znacheniya dzeta-funktsii Rimana v tselykh tochkakh”, Respublikanskaya nauchno-teoreticheskaya konferentsiya “Teoriya chisel i ee prilozheniya”, Tezisy dokl. (Tashkent, 26–28 sentyabrya 1990 g.), Tashkentskii gospedinstitut, Tashkent, 1990, 27

[3] Vasilyev D. V., On small linear forms for the values of the Riemann zeta-function at odd integers, Preprint No 1 (558), Nat. Acad. Sci. Belarus, Institute Math., Minsk, 2001

[4] Zudilin V. V., “Sovershenno uravnoveshennye gipergeometricheskie ryady i kratnye integraly”, UMN, 57:4 (2002), 177–178 | MR | Zbl

[5] Sorokin V. N., “Teorema Aperi”, Vestn. MGU. Ser. 1. Matem., mekh., 1998, no. 3, 48–52 | MR | Zbl

[6] Sorokin V. N., “O mere transtsendentnosti chisla $\pi^2$”, Matem. sb., 187:12 (1996), 87–120 | MR | Zbl

[7] Zlobin S. A., “Integraly, predstavlyaemye v vide lineinykh form ot obobschennykh polilogarifmov”, Matem. zametki, 71:5 (2002), 782–787 | MR | Zbl

[8] Fischler S., “Formes linéaires en polyzêtas et intégrales multiples”, C. R. Acad. Sci. Paris Sér. I Math., 335 (2002), 1–4 | MR | Zbl

[9] Zlobin S. A., “O nekotorykh integralnykh tozhdestvakh”, UMN, 57:3 (2002), 153–154 | MR | Zbl

[10] Hoang Ngoc Minh, Petitot M., Van Der Hoeven J., Discrete Math., 225:1–3 (2000), 217–230 | Zbl

[11] Ulanskii E. A., “Tozhdestva dlya obobschennykh polilogarifmov”, Matem. zametki, 73:4 (2003), 613–624 | Zbl

[12] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989

[13] Vasilev D. V., “Nekotorye formuly dlya dzeta-funktsii Rimana v tselykh tochkakh”, Vestn. MGU. Ser. 1. Matem., mekh., 1996, no. 1, 81–84