D sets and a Sárközy theorem for countable fields
We establish that if ℱ is a countable field of characteristic p, U is a unitary action of ℱℓ on a Hilbert space ℋ, and P is an essential idempotent ultrafilter on ℱ, then for every polynomial r: ℱ → ℱℓ with r(0) = 0 one has (Formula Presented), where Pr is the projection onto the closed subspace (Formula Presented). We then derive combinatorial consequences of this result, including results for sufficiently large finite fields.
Israel Journal of Mathematics
McCutcheon, R., & Windsor, A. (2014). D sets and a Sárközy theorem for countable fields. Israel Journal of Mathematics, 201 (1), 123-146. https://doi.org/10.1007/s11856-014-1062-7