Julia Brandes: A minimalist approach to the circle method and Diophantine problems over thin sets

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.