### Efficient congruencing in ellipsephic sets

Linfoot Number Theory Seminar

16th May 2018, 11:00 am – 12:00 pm

Howard House, 4th Floor Seminar Room

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.

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