Irrationality measures of Carlitz zeta values in characteristic \(p\) (Q687529)

Let \(\mathbf{A}= \mathbb{F}_ q[T]\) and put \(\mathbf{K}= \mathbb{F}_ q((q/T))\). Thus \textbf{A} is discrete and compact in \textbf{K}. Let \(i\) be a positive integer. One puts \(\zeta_{\mathbf{A}}(i)= \sum_{n\text{ monic in \textbf{A}}}n^{-i}\). One knows that these sums converge in \textbf{K} to elements which are transcendental over \(\mathbf{k}=\mathbb{F}_ q(T)\). In the paper being reviewed, exact measures of irrationality are calculated for certain of these zeta values.