Integral identities and constructions of approximations to zeta-values
Yuri V. Nesterenko
Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 2, pp. 535-550.

Nous présentons une construction générale de combinaisons linéaires à coefficients rationnels en les valeurs de la fonction zêta de Riemann aux entiers. Ces formes linéaires sont exprimées en termes d'intégrales complexes, dites de Barnes, ce qui permet de les estimer. Nous montrons quelques identités reliant ces intégrales à des intégrales multiples sur le cube unité réel.

Some general construction of linear forms with rational coefficients in values of Riemann zeta-function at integer points is presented. These linear forms are expressed in terms of complex integrals of Barnes type that allows to estimate them. Some identity connecting these integrals and multiple integrals on the real unit cube is proved.

@article{JTNB_2003__15_2_535_0,
     author = {Nesterenko, Yuri V.},
     title = {Integral identities and constructions of approximations to zeta-values},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {535--550},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {2},
     year = {2003},
     doi = {10.5802/jtnb.412},
     zbl = {02184610},
     mrnumber = {2140866},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.412/}
}
Yuri V. Nesterenko. Integral identities and constructions of approximations to zeta-values. Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 2, pp. 535-550. doi : 10.5802/jtnb.412. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.412/

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