Multiple integrals and linear forms in zeta-values

Abstract

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.