English

Decoupling inequalities for short generalized Dirichlet sequences

Classical Analysis and ODEs 2023-12-20 v2 Number Theory

Abstract

We study decoupling theory for functions on R\mathbb{R} with Fourier transform supported in a neighborhood of short Dirichlet sequences {logn}n=N+1N+N1/2\{\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.

Keywords

Cite

@article{arxiv.2104.00856,
  title  = {Decoupling inequalities for short generalized Dirichlet sequences},
  author = {Yuqiu Fu and Larry Guth and Dominique Maldague},
  journal= {arXiv preprint arXiv:2104.00856},
  year   = {2023}
}

Comments

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

R2 v1 2026-06-24T00:47:43.614Z