Linear forms in zeta values arising from certain Sorokin-type integrals
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 5, pp. 161-172.

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

This paper deals with certain multiple integrals which can be represented as linear forms of zeta values with rational coefficients.
@article{FPM_2010_16_5_a11,
     author = {T. Rivoal},
     title = {Linear forms in zeta values arising from certain {Sorokin-type} integrals},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {161--172},
     publisher = {mathdoc},
     volume = {16},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a11/}
}
TY  - JOUR
AU  - T. Rivoal
TI  - Linear forms in zeta values arising from certain Sorokin-type integrals
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2010
SP  - 161
EP  - 172
VL  - 16
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a11/
LA  - ru
ID  - FPM_2010_16_5_a11
ER  - 
%0 Journal Article
%A T. Rivoal
%T Linear forms in zeta values arising from certain Sorokin-type integrals
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2010
%P 161-172
%V 16
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a11/
%G ru
%F FPM_2010_16_5_a11
T. Rivoal. Linear forms in zeta values arising from certain Sorokin-type integrals. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 5, pp. 161-172. http://geodesic.mathdoc.fr/item/FPM_2010_16_5_a11/

[1] Vasilev D. V., “Approksimatsii nulya lineinymi formami ot znachenii dzeta-funktsii Rimana”, Dokl. Nats. akad. nauk Belarusi, 45:5 (2001), 36–40 | MR | Zbl

[2] Gutnik L. A., “Ob irratsionalnosti nekotorykh velichin, soderzhaschikh $\zeta(3)$”, Uspekhi mat. nauk, 34:3 (1979), 190 | MR | Zbl

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

[4] Zlobin S. A., “O nekotorykh integralnykh tozhdestvakh”, Uspekhi mat. nauk, 57:3 (2002), 153–154 | DOI | MR | Zbl

[5] Nesterenko Yu. V., “Nekotorye zamechaniya o $\zeta(3)$”, Mat. zametki, 59:6 (1996), 865–880 | DOI | MR | Zbl

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

[7] Apéry R., “Irrationalité de $\zeta(2)$ et $\zeta(3)$”, Astérisque, 61 (1979), 11–13 | MR | Zbl

[8] Ball K., Rivoal T., “Irrationalité d'une infinité de valeurs de la fonction zêta aux entiers impairs”, Invent. Math., 146:1 (2001), 193–207 | DOI | MR | Zbl

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

[10] Beukers F., “Padé-approximations in number theory”, Padé Approximation and Its Applications, Proc. Conference (Amsterdam, The Netherlands, October 29–31, 1980), Lect. Notes Math., 888, eds. M. G. de Bruin, H. van Rossum, Springer, Berlin, 1981, 90–99 | DOI | MR

[11] Cresson J., Fischler S., Rivoal T., “Phénomènes de symétrie dans des formes linéaires en polyzêtas”, J. Reine Angew. Math., 617 (2008), 109–151 | DOI | MR | Zbl

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

[13] Cresson J., Fischler S., Rivoal T. http://www.math.u-psud.fr/~fischler/algo.html

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

[15] Fischler S., “Multiple series connected to Hoffman's conjecture on multiple zeta values”, J. Algebra, 320 (2008), 1682–1703 | DOI | MR | Zbl

[16] Krattenthaler C., Rivoal T., “An identity of Andrews, multiple integrals, and very-well-poised hypergeometric series”, Ramanujan J., 13:1–3 (2007), 203–219 | DOI | MR | Zbl

[17] Krattenthaler C., Rivoal T., Hypergéométrie et fonction zêta de Riemann, Mem. Amer. Math. Soc., 186, Amer. Math. Soc., 2007 | MR

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

[19] Rhin G., Viola C., “On a permutation group related to $\zeta(2)$”, Acta Arith., 77 (1996), 23–56 | MR | Zbl

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

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

[22] Rivoal T., “La fonction zêta de Riemann prend une infinité de valeurs irrationnelles aux entiers impairs”, C. R. Acad. Sci. Paris. Sér. I. Math., 331:4 (2000), 267–270 | DOI | MR | Zbl

[23] Rivoal T., “Irrationalité d'au moins un des neuf nombres $\zeta(5),\zeta(7),\dots,\zeta(21)$”, Acta Arith., 103:2 (2002), 157–167 | DOI | MR | Zbl

[24] Rivoal T., “Valeurs aux entiers de la fonction zêta de Riemann”, Quadrature, 49 (2003), 35–41 http://www-fourier.ujf-grenoble.fr/~rivoal/articles/quaddefi.pdf

[25] Zudilin W., “Well-poised hypergeometric service for diophantine problems of zeta values”, J. Théor. Nombres Bordeaux, 15:2 (2003), 593–626 | DOI | MR | Zbl

[26] Zudilin W., “Arithmetic of linear forms involving odd zeta values”, J. Théor. Nombres Bordeaux, 16 (2004), 251–291 | DOI | MR | Zbl