Homemath.NTarXiv:2605.29470

The weighted large sieve through Parseval

math.NT2026-05v1license

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}
}