Year: 2026
Type: preprint
Abstract: Let $n \geq 3$. 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 $n \geq 3$.
Source: arXiv (Cornell University)
Author: de Faveri, Alexandre
Institution: École Polytechnique Fédérale de Lausanne
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220739762