PreprintCC BY-NC-SA 4.0arXiv
The weighted large sieve through Parseval
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. We compute in passing the L2-norm of the Beurling-Selberg majorant of the characteristic function of an interval.
Related
- The large sieve through Parseval, Large sifted sets are regular
- Optimal large sieve for fixed order characters
- Luo's Spectral Large Sieve Inequality on Short Intervals
- Optimization of Quadratic Sieve Algorithm Implementation for Large Integer Factorization
- The large sieve inequality and additive decompositions of sums of squares
BibTeX
@misc{ramare2026weighted,
title = {{The weighted large sieve through Parseval}},
author = {Olivier Ramaré},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25885},
eprint = {2609.25885},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25885},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - The weighted large sieve through Parseval
AU - Olivier Ramaré
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25885
UR - https://arxiv.org/abs/2609.25885
AB - 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. We compute in passing the L^2-norm of the Beurling-Selberg majorant of the characteristic function of an interval.
ER -