Abstract
Let Fq be the finite field with q elements. We consider the number of pairs (f1,f2) with f1f2 being a cube, where fi∈Fq[T] and degfi=n for i=1,2. By contour integration, we obtain an asymptotic formula in terms of either n or q. This is a polynomial analogue of a result for integers due to de la Bretèche, Kurlberg and Shparlinski [2].
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