Partition regularity of \(x+y=z^2\) over \(\mathbb{F}_p\)

Sofia Lindqvist (Oxford)

Frank Adams 1,

We show that given a \(k\)-colouring of \(\mathbb{F}_p\) there are monochromatic \(x,y,z\), not all equal, such that \(x+y=z^2\), provided \(p\) is large enough in terms of \(k\). The proof uses methods developed by Green and Sanders for dealing with partition regularity of the configuration \(\{x,y,x+y,xy\}\). In particular the proof uses Fourier analysis, an arithmetic regularity lemma and a quantitative linear Ramsey result.
Import this event to your Outlook calendar
▲ Up to the top