Geodesic
On the equivalence of Beukers-type and Sorokin-type multiple integrals
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 5, pp. 49-59.

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

It is well known that a triple Beukers-type integral, as defined by G. Rhin and C. Viola, can be transformed into a suitable triple Sorokin-type integral. I will discuss possible extensions to the $n$-dimensional case of a similar equivalence between suitably defined Beukers-type and Sorokin-type multiple integrals, with consequences on the arithmetical structure of such integrals as linear combinations of zeta-values with rational coefficients. 
@article{FPM_2010_16_5_a4,
     author = {C. Viola},
     title = {On the equivalence of {Beukers-type} and {Sorokin-type} multiple integrals},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {49--59},
     publisher = {mathdoc},
     volume = {16},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a4/}
}
TY  - JOUR
AU  - C. Viola
TI  - On the equivalence of Beukers-type and Sorokin-type multiple integrals
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2010
SP  - 49
EP  - 59
VL  - 16
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a4/
LA  - ru
ID  - FPM_2010_16_5_a4
ER  - 
%0 Journal Article
%A C. Viola
%T On the equivalence of Beukers-type and Sorokin-type multiple integrals
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2010
%P 49-59
%V 16
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a4/
%G ru
%F FPM_2010_16_5_a4
C. Viola. On the equivalence of Beukers-type and Sorokin-type multiple integrals. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 5, pp. 49-59. http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a4/

[1] Sorokin V. N., “Teorema Aperi”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1998, no. 3, 48–53 | MR | Zbl

[2] Cresson J., Fischler S., Rivoal T., “Séries hypergéométriques multiples et polyzêtas”, Bull. Soc. Math. France, 136:1 (2008), 97–145 | MR | Zbl

[3] Fischler S., “Groupes de Rhin–Viola et intégrales multiples”, J. Théor. Nombres Bordeaux, 15:2 (2003), 479–534 | DOI | MR | Zbl

[4] Nesterenko Yu. V., “Integral identities and constructions of approximations to zeta-values”, J. Théor. Nombres Bordeaux, 15 (2003), 535–550 | DOI | MR | Zbl

[5] Rhin G., Viola C., “The group structure for $\zeta(3)$”, Acta Arith., 97:3 (2001), 269–293 | DOI | MR | Zbl

[6] Rhin G., Viola C., “Multiple integrals and linear forms in zeta-values”, Funct. Approx., 37 (2007), 429–444 | DOI | MR | Zbl

[7] Viola C., “The arithmetic of Euler's integrals”, Riv. Mat. Univ. Parma (7), 3$^*$ (2004), 119–149 | MR | Zbl