Remarks on irrationality of q-harmonic series

摘要

We sharpen the known irrationality measures for the quantities , where z ? {±1} and p ?ℤ {0, ±1}. Our construction of auxiliary linear forms gives a q-analogue of the approach recently applied to irrationality problems for the values of the Riemann zeta function at positive integers. We also present a method for improving estimates of the irrationality measures of q-series.