On Waring's Problem: Two Cubes and Two Minicubes (1006.5142v1)

Abstract: We establish that almost every positive integer $n$ is the sum of four cubes, two of which are at most $n^{\theta}$, as long as $\theta\geq192/869$. An asymptotic formula for the number of such representations is established when $1/4<\theta<1/3$.