Primes in the Chebotarev density theorem for all number fields

Abstract: Let $L/K$ be a Galois extension of number fields such that $L\not=\mathbb{Q}$, and let $C$ be a conjugacy class in the Galois group of $L/K$. We show that there exists an unramified prime $\mathfrak{p}$ of $K$ such that $\sigma_{\mathfrak{p}}=C$ and $N \mathfrak{p} \le d_{L}^{B}$ with $B= 310$. This improves a previous result of Ahn and Kwon, who showed that $B=12\,577$ is admissible. The main tool is a stronger Deuring-Heilbronn (zero-repulsion) phenomenon. We also use Fiori's numerical verification for a finite list of fields. This is joint work with Peng-Jie Wong (NCTS, Taiwan).

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: Description: Research/departmental seminar

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