12 citations · 44 across the 14 of their papers we have counts for
4 papers · 1 filter
Solving equations in dense Sidon sets
Sean Prendiville
We offer an alternative proof of a result of Conlon, Fox, Sudakov and Zhao on solving translation-invariant linear equations in dense Sidon sets. Our proof generalises to equations…
The inverse theorem for the nonlinear Roth configuration: an exposition
Sean Prendiville
We give an exposition of the inverse theorem for the cut-norm associated to the nonlinear Roth configuration, established previously by Peluse and the author.
Counting monochromatic solutions to diagonal Diophantine equations
Sean Prendiville
We show how to adapt the Hardy--Littlewood circle method to count monochromatic solutions to diagonal Diophantine equations. This delivers a lower bound which is optimal up to abso…
A polylogarithmic bound in the nonlinear Roth theorem
Sarah Peluse, Sean Prendiville
We show that sets of integers lacking the configuration , , have at most polylogarithmic density.