Vinogradov estimates applied to maximal theorems related to Waring's problem

Vinogradov estimates applied to maximal theorems related to Waring's problem

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Kevin Hughes, Princeton University
Fine Hall 314

I'll discuss the discrete spherical maximal function of Magyar--Stein--Wainger and it's estimates. Then I'll prove recent results for higher degrees which use Vinogradov type estimates for exponential sums to improve results about maximal functions defined on the hypersurfaces arising in Waring's problem.