We refine (and give a new proof of) Nesterenko’s famous linear independence criterion from 1985, by making use of the fact that some coefficients of linear forms may have large common divisors. This is a typical situation appearing in the context of hypergeometric constructions of Q-linear forms involving zeta values or their q-analogs. We apply our criterion to sharpen previously known results in this direction.
Mathematische Annalen Vol. 347, Issue 4, p. 739-763