Speaker
Julia Brandes, University of Gothenburg
Abstract
Even though additive problems such as Waring’s problem are usually treated over the integers, there is a not insignificant body of work studying additive questions over other sets. We confirm in quantitative terms the well-known heuristic that a mean value estimate and an estimate of Weyl type, together with suitable distribution properties of the underlying set over a set of admissible residue classes, are sufficient to implement the circle method. This allows us to give a rather general proof of Waring’s problem which is applicable to a range of sufficiently well-behaved thin sets.