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I have a very general, and possibly not very precisely stated question, which comes up quite often in my work, and I would be very happy to be able to address. To my dismay, I only have some very ...

Let $q$ be a power of a prime $p$. For every $i\in\mathbb N$, one denotes $D_i=\prod_{\substack{h\in\mathbb F_q[T]\text{ monic}\\\deg h=i}}\limits h$. For $n\in\mathbb N$, write $$n=n_0+n_1q+\cdots+...