Kirsti Biggs

Efficient congruencing in ellipsephic sets

An ellipsephic set is a subset of the natural numbers whose elements have digital restrictions in some fixed base. We obtain discrete restriction estimates for mean values of exponential sums over ellipsephic sets – equivalently, we bound the number of solutions to a Vinogradov system of equations – using a version of Wooley’s efficient congruencing method. In this talk, I will outline the key ideas from the proof, give motivating examples, and discuss potential applications to Waring’s problem over ellipsephic sets.