Structure and paucity in affine diagonal systems, I

Julia Brandes, Trevor D. Wooley

Let $\epsilon >0$ and $\mathbf{h}\in {\mathbb{Z}}^3$. We show that whenever $P$ is large and the system \[ x_1^j+x_2^j-y_1^j-y_2^j=h_j\quad (j=1,2,3) \] has more than $P^{\epsilon }$…