Simultaneous polynomial recurrence
Simultaneous polynomial recurrence
Let A ⊆ {1, …, N} and P1, …, Pℓ ∈ ℤ[n] with Pi(0) = 0 and deg Pi = k for every 1 ⩽ i ⩽ ℓ. We show, using Fourier analytic techniques, that, for every ε > 0, there necessarily exists n ∈ ℕ such that | A …