Discrete Fourier restriction via efficient congruencing: basic principles

Trevor D. Wooley

We show that whenever $s>k(k+1)$, then for any complex sequence $({\mathfrak{a}}_n{)}_{n\in \mathbb{Z}}$, one has $$\int_{[0,1)^k}\left| \sum_{|n|\le N}\mathfrak a_ne(α_1n+\ldots +α_kn^k…