Multiple integrals and linear forms in zeta-values

We deflne n-dimensional Beukers-type integrals over the unit hypercube. Using an n-dimensional birational transformation we show that such integrals are equal to suita- ble n-dimensional Sorokin-type integrals with linear constraints, and represent linear forms in 1;‡(2);‡(3);:::;‡(n) with rational coe-cients. Keywords: Multiple integrals of rational functions, values of the Riemann zeta-function, bira- tional transformations.