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 with Fourier transform supported in a neighborhood of short Dirichlet sequences , as well as sequences with similar convexity properties. We utilize the wave packet structure of functions with frequency support near an arithmetic progression.
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