The weighted large sieve through Parseval
Number Theory
2026-05-29 v1
Abstract
We modify the approach to the arithmetical form of the large sieve by relying on the Parseval identity rather than on an approximate Bessel inequality and as a consequence, improve on the weighted large sieve inequality beyond what was heuristically accessible by the earlier approach. We also discuss the optimality of this approach.
Cite
@article{arxiv.2605.29470,
title = {The weighted large sieve through Parseval},
author = {Olivier Ramaré},
journal= {arXiv preprint arXiv:2605.29470},
year = {2026}
}