30 citations · 81 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
Diophantine equations in the primes
Brian Cook, Ákos Magyar
Let be a system of polynomials with integer coefficients of degree in variables . For a giv…
A Multidimensional Szemerédi Theorem in the primes
Brian Cook, Ákos Magyar, Tatchai Titichetrakun
Let be a subset of positive relative upper density of $\PP^d$, the -tuples of primes. We prove that contains an affine copy of any finite set $F\subs\Z^d$, which provide…
On restricted arithmetic progressions over finite fields
Brian Cook, Akos Magyar
Let A be a subset of $\F_p^n$, the -dimensional linear space over the prime field $\F_p$ of size at least $\de N$ , and let be the level set of a homoge…
Constellations in P^d
Brian Cook, Akos Magyar
Let A be a subset of positive relative upper density of P^d, the d-tuples of primes. We prove that A contains an affine copy of any finite set of lattice points E, as long as E is…
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…