We sharpen the known irrationality measures for the quantities ∑ from v = 1 to ∞ of (z~(v-1))/(p~v - 1), 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.
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