Brian Cook

activity

20092020

most citedDiophantine equations in the primes

30 citations · 81 across the 9 of their papers we have counts for

collaborators

14 papers

math.CA2020★ 7 cited

Multilinear maximal operators associated to simplices

Brian Cook, Neil Lyall, Akos Magyar

We establish $L^{p_{1}} \times \dots \times L^{p_{k}} \to L^{r}$ and $ℓ^{p_{1}} \times \dots \times ℓ^{p_{k}} \to ℓ^{r}$ type bounds for multilinear maximal operators associated to averages…

math.CA2020

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…

math.CA2019

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…

math.CA2018

A note on discrete spherical averages over sparse sequences

Brian Cook

This note presents an example of an increasing sequence $(λ_{l})_{l = 1}^{\infty}$ such that the maximal operators associated to normalized discrete spherical convolution averages \[ \su…

math.CA2018★ 3 cited

Discrete multilinear spherical averages

Brian Cook

In this note we give a characterization of $ℓ^{p} \times ... \times ℓ^{p} \to ℓ^{q}$ boundedness of maximal operators associated to multilinear convolution averages over spheres…

math.NT2017

Maximal Function Inequalities and a Theorem of Birch

Brian Cook

In this paper we prove an analogue of the discrete spherical maximal theorem of Magyar, Stein, and Wainger, an analogue which concerns maximal functions associated to homogenous al…