Brian Cook

activity

20092020

most citedDiophantine equations in the primes

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

collaborators

Showing 2017Show all

3 papers · 1 filter

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…

math.CA2017★ 16 cited

Improved $ℓ^{p}$ -Boundedness for Integral $k$ -Spherical Maximal Functions

Theresa C. Anderson, Brian Cook, Kevin Hughes +1

We improve the range of $ℓ^{p} (Z^{d})$ -boundedness of the integral $k$ -spherical maximal functions introduced by Magyar. The previously best known bounds for the full $k$ -sp…

math.CA2017

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…

Maximal Function Inequalities and a Theorem of Birch

Improved ℓp-Boundedness for Integral k-Spherical Maximal Functions

On the ergodic Waring--Goldbach problem

Improved $ℓ^{p}$ -Boundedness for Integral $k$ -Spherical Maximal Functions