3 citations · 10 across the 20 of their papers we have counts for
4 papers · 1 filter
Sharp Transitions in Making Squares
Ernie Croot, Andrew Granville, Robin Pemantle +1
In many integer factoring algorithms, one produces a sequence of integers (created in a pseudo-random way), and wishes to rapidly determine a subsequence whose product is a square…
On rich lines in grids
Evan Borenstein, Ernie Croot
In this paper we show that if one has a grid A x B, where A and B are sets of n real numbers, then there can be only very few ``rich'' lines in certain quite small families. Indeed…
On a certain generalization of the Balog-Szemeredi-Gowers Theorem
Ernie Croot, Evan Borenstein
In this note, we prove a certain hypergraph generalization of the Balog-Szemeredi-Gowers Theorem. Our result shares some features in common with a similar such generalizsation due…
A new proof of Roth's theorem on arithmetic progressions
Ernie Croot, Olof Sisask
We present a proof of Roth's theorem that follows a slightly different structure to the usual proofs, in that there is not much iteration. Although our proof works using a type of…