Irrationality of ζq(1) and ζq(2)

In this paper we show how one can obtain simultaneous rational approximants for ζq(1) and ζq(2) with a common denominator by means of Hermite–Padé approximation using multiple little q-Jacobi polynomials and we show that properties of these rational approximants prove that 1, ζq(1), ζq(2) are linearly independent over Q. In particular this implies that ζq(1) and ζq(2) are irrational. Furthermore we give an upper bound for the measure of irrationality.