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.

Publication Title

Israel Journal of Mathematics