Geodesic
Properties of coefficients of certain linear forms in generalized polylogarithms
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 41-58.

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

We study properties of coefficients of a linear form originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers. 
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S. A. Zlobin. Properties of coefficients of certain linear forms in generalized polylogarithms. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 6, pp. 41-58. http://geodesic.mathdoc.fr/item/FPM_2005_11_6_a5/

[1] Vasilev D. V., O malykh lineinykh formakh ot znachenii dzeta-funktsii Rimana v nechetnykh tochkakh, Preprint No 1(558), NAN Belarusi, In-t matematiki, Minsk, 2000

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

[3] Zlobin S. A., “Proizvodyaschie funktsii dlya znachenii kratnoi dzeta-funktsii”, Vestn. Mosk. un-ta. Ser. 1, Matematika, mekhanika, 2005, no. 2, 55–59 | MR | Zbl

[4] Zlobin S. A., “Razlozheniya kratnykh integralov v lineinye formy”, Mat. zametki, 77:5 (2005), 683–706 | MR | Zbl

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

[6] Prasolov V. V., Mnogochleny, MTsNMO, M., 1999

[7] Fuks B. A., Vvedenie v teoriyu analiticheskikh funktsii mnogikh kompleksnykh peremennykh, Fizmatgiz, M., 1962 | MR

[8] 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

[9] Krattenthaler C., Rivoal T., Hypergéométrie et fonction zêta de Riemann, arXiv: /math.NT/0311114 | MR