Trevor Wooley

A certain octonary cubic form

We apply the circle method to obtain an asymptotic formula for the number of integral points on a certain sliced cubic hypersurface related to the Segre cubic. Unusually, the major and minor arc integrals in this application are both positive and of the same order of magnitude. This vindicates and generalises a line of thought pursued by Hooley in the case of certain diagonal cubic equations in 6 variables, and a circle method philosophy described in 1995 by Vaughan and the author in a paper concerning a certain nonary cubic form. This is work joint with Joerg Bruedern.