Fast polynomial multiplication on a GPU

We present CUDA implementations of Fast Fourier Transforms over finite fields. This allows us to develop GPU support for dense univariate polynomial multiplication leading to speedup factors in the range 21 - 37 with respect to the best serial C-code available to us, for our largest input data sets. Since dense univariate polynomial multiplication is a core routine in symbolic computation, this is promising result for the integration of GPU support into computer algebra systems.