Multiple integrals and linear forms in zeta-values
Rhin, Georges ; Viola, Carlo
Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, p. 429-444 / Harvested from Project Euclid
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We define $n$-dimensional Beukers-type integrals over the unit hypercube. Using an $n$-dimensional birational transformation we show that such integrals are equal to suitable $n$-dimensional Sorokin-type integrals with linear constraints, and represent linear forms in $1, \zeta(2), \zeta(3), \dots, \zeta(n)$ with rational coefficients.
Publié le : 2007-09-15
Classification:  multiple integrals of rational functions,  values of the Riemann zeta-function,  birational transformations,  11J72,  11M06 
@article{1229619663,
     author = {Rhin, Georges and Viola, Carlo},
     title = {Multiple integrals and linear forms in zeta-values},
     journal = {Funct. Approx. Comment. Math.},
     volume = {37},
     number = {1},
     year = {2007},
     pages = { 429-444},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229619663}
}

Rhin, Georges; Viola, Carlo. Multiple integrals and linear forms in zeta-values. Funct. Approx. Comment. Math., Tome 37 (2007) no. 1, pp.  429-444. http://gdmltest.u-ga.fr/item/1229619663/