PreprintarXiv licencearXiv
Optimal large sieve for fixed order characters
Abstract
Let n ≥ 3. We improve the large sieve inequality for n-th order Hecke characters over any number field containing the n-th roots of unity. Our bound is expected to be optimal in all ranges of parameters. Several applications are deduced, including a tight upper bound for the second moment of cubic characters ordered by conductor, asymptotics with lower order terms for the cubic second moment over squarefree moduli, and improved moment and zero density estimates for every n ≥ 3.
Related
- Inventory Policies with Returns and Demand Uncertainty: Optimal, Fixed-Quantity, and Order Cancellation Models
- On the (in)finiteness of fixed characters in genus $3$
- Coprime Actions and Characters Non-vanishing on the Fixed-point Subgroup
- The weighted large sieve through Parseval
- The large sieve through Parseval, Large sifted sets are regular
BibTeX
@misc{faveri2026optimal,
title = {{Optimal large sieve for fixed order characters}},
author = {Alexandre de Faveri},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04045},
eprint = {2610.04045},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04045},
}
RIS
TY - UNPB
TI - Optimal large sieve for fixed order characters
AU - Alexandre de Faveri
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.04045
UR - https://arxiv.org/abs/2610.04045
AB - Let n ≥ 3. We improve the large sieve inequality for n-th order Hecke characters over any number field containing the n-th roots of unity. Our bound is expected to be optimal in all ranges of parameters. Several applications are deduced, including a tight upper bound for the second moment of cubic characters ordered by conductor, asymptotics with lower order terms for the cubic second moment over squarefree moduli, and improved moment and zero density estimates for every n ≥ 3.
ER -