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.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 arXiv:
 arXiv:2104.00856
 Bibcode:
 2021arXiv210400856F
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Number Theory
 EPrint:
 54 pages