Linear forms from the Gowers uniformity norm
This is a companion note to our paper 'A relative Szemerédi theorem', elaborating on a concluding remark. In that paper, we showed how to prove a relative Szemerédi theorem for (r + 1)-term arithmetic progressions assuming a linear forms condition. Here we show how to replace this condition with an assumption about the Gowers uniformity norm U^r.
Submitted - 1305.5565.pdf