A minimalist version of the circle method and Diophantine problems over thin sets
Number Theory Seminar
Date
Wednesday, June 10, 2026 13:00 - 14:30
Speaker
Julia Brandes (University of Gothenburg)
Location
Central Bldg / O1 / Mondi 2a (I01.O1.008)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar
Host
Tim Browning
Contact
We study the minimal conditions under which we can establish asymptotic formulae for Waring's problem and other additive problems that may be tackled by the circle method. 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.