Decoupling inequalities for short generalized Dirichlet sequences

Abstract

We study decoupling theory for functions on $\mathbb{R}$ with Fourier transform supported in a neighborhood of short Dirichlet sequences $\{\log n{\}}_{n=N+1}^{N+N^{1/2}}$, as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression.

54 pages; added small-cap type decoupling; included a transference argument, which we learned from James Maynard, that implies corollaries on $L^p$ estimates for short generalized Dirichlet sequences from parabola decoupling

References in corpus (1)

• Improved decoupling for the parabola

Cited by in corpus (1)

• Incidence estimates for $\alpha$-dimensional tubes and $\beta$-dimensional balls in ${\mathbb{R}}^2$