Abstract
Very recently, Nesterenko proved a p-adic analogue of his famous dimension estimate from 1985. The main aim of our present paper is to use this criterion to obtain lower bounds for the dimension of ℚ-vector spaces spanned by the values at certain rational points of p-adic solutions of a class of linear q-difference equations. For the application of Nesterenko's new estimate, we first need a p-adic analogue of Töpfer's results on entire solutions of such functional equations, and secondly, very precise evaluations of certain p-adic Schnirelman integrals.
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