Publications (18)
A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem
Brian Cook, Kevin Hughes, Zane Kun Li +3
We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely…
Multilinear maximal operators associated to simplices
Brian Cook, Neil Lyall, Akos Magyar
We establish and type bounds for multilinear maximal operators associated to averages…
Torsion points on elliptic curves with complex multiplication
Pete L. Clark, Brian Cook, James Stankewicz
We present seven theorems on the structure of prime order torsion points on CM elliptic curves defined over number fields. The first three results refine bounds of Silverberg and P…
Bounds for Lacunary maximal functions given by Birch--Magyar averages
Brian Cook, Kevin Hughes
We obtain positive and negative results concerning lacunary discrete maximal operators defined by dilations of sufficiently nonsingular hypersurfaces arising from Diophantine equat…
On the ergodic Waring--Goldbach problem
Theresa C. Anderson, Brian Cook, Kevin Hughes +1
We prove an asymptotic formula for the Fourier transform of the arithmetic surface measure associated to the Waring--Goldbach problem and provide several applications, including bo…
Supercritical discrete restriction estimates for forms in many variables
Brian Cook, Kevin Hughes, Eyvindur Palsson
We prove discrete restriction estimates for a broad class of hypersurfaces and varieties of intermediate codimension. For our result about hypersurfaces, we use Bourgain's arithmet…